I found this coding too convoluted, so I rewrote it in a different way.
You tests pass with this, but I admit I haven't double-checked them yet;
I'll do that next.

I don't think we need to give a NOTICE when the trigger name does not
match; it doesn't really matter that the trigger was named differently
before the command, does it?

-- 
Álvaro Herrera           39°49'30"S 73°17'W  —  https://www.EnterpriseDB.com/
diff --git a/src/backend/commands/trigger.c b/src/backend/commands/trigger.c
index 6d4b7ee92a..da6320f6a1 100644
--- a/src/backend/commands/trigger.c
+++ b/src/backend/commands/trigger.c
@@ -71,6 +71,10 @@ int			SessionReplicationRole = SESSION_REPLICATION_ROLE_ORIGIN;
 static int	MyTriggerDepth = 0;
 
 /* Local function prototypes */
+static void renametrig_internal(Relation tgrel, Relation targetrel,
+								HeapTuple trigtup, const char *newname);
+static void renametrig_partition(Relation tgrel, Oid partitionId,
+								 Oid parentTriggerOid, const char *newname);
 static void SetTriggerFlags(TriggerDesc *trigdesc, Trigger *trigger);
 static bool GetTupleForTrigger(EState *estate,
 							   EPQState *epqstate,
@@ -1441,6 +1445,14 @@ renametrig(RenameStmt *stmt)
 	/* Have lock already, so just need to build relcache entry. */
 	targetrel = relation_open(relid, NoLock);
 
+	/*
+	 * On partitioned tables, this operation recurses to partitions, unless
+	 * caller requested not to.  Lock all tables upfront, if needed.
+	 */
+	if (stmt->relation->inh &&
+		targetrel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
+		(void) find_all_inheritors(relid, AccessExclusiveLock, NULL);
+
 	/*
 	 * Scan pg_trigger twice for existing triggers on relation.  We do this in
 	 * order to ensure a trigger does not exist with newname (The unique index
@@ -1489,27 +1501,25 @@ renametrig(RenameStmt *stmt)
 	{
 		Form_pg_trigger trigform;
 
-		/*
-		 * Update pg_trigger tuple with new tgname.
-		 */
-		tuple = heap_copytuple(tuple);	/* need a modifiable copy */
 		trigform = (Form_pg_trigger) GETSTRUCT(tuple);
 		tgoid = trigform->oid;
 
-		namestrcpy(&trigform->tgname,
-				   stmt->newname);
+		/* Rename the trigger on this relation ... */
+		renametrig_internal(tgrel, targetrel, tuple, stmt->newname);
 
-		CatalogTupleUpdate(tgrel, &tuple->t_self, tuple);
+		/* ... and if it is partitioned, recurse to its partitions */
+		if (stmt->relation->inh &&
+			targetrel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
+		{
+			PartitionDesc partdesc = RelationGetPartitionDesc(targetrel, true);
 
-		InvokeObjectPostAlterHook(TriggerRelationId,
-								  tgoid, 0);
+			for (int i = 0; i < partdesc->nparts; i++)
+			{
+				Oid		partitionId = partdesc->oids[i];
 
-		/*
-		 * Invalidate relation's relcache entry so that other backends (and
-		 * this one too!) are sent SI message to make them rebuild relcache
-		 * entries.  (Ideally this should happen automatically...)
-		 */
-		CacheInvalidateRelcache(targetrel);
+				renametrig_partition(tgrel, partitionId, trigform->oid, stmt->newname);
+			}
+		}
 	}
 	else
 	{
@@ -1533,6 +1543,92 @@ renametrig(RenameStmt *stmt)
 	return address;
 }
 
+/*
+ * Subroutine for renametrig -- perform the actual work of renaming one
+ * trigger on one table.
+ */
+static void
+renametrig_internal(Relation tgrel, Relation targetrel, HeapTuple trigtup,
+					const char *newname)
+{
+	HeapTuple	tuple;
+	Form_pg_trigger newtgform;
+
+	/*
+	 * Update pg_trigger tuple with new tgname.
+	 */
+	tuple = heap_copytuple(trigtup);	/* need a modifiable copy */
+	newtgform = (Form_pg_trigger) GETSTRUCT(tuple);
+
+	namestrcpy(&newtgform->tgname, newname);
+
+	CatalogTupleUpdate(tgrel, &tuple->t_self, tuple);
+
+	InvokeObjectPostAlterHook(TriggerRelationId, newtgform->oid, 0);
+
+	/*
+	 * Invalidate relation's relcache entry so that other backends (and
+	 * this one too!) are sent SI message to make them rebuild relcache
+	 * entries.  (Ideally this should happen automatically...)
+	 */
+	CacheInvalidateRelcache(targetrel);
+}
+
+/*
+ * Subroutine for renametrig -- Helper for recursing to partitions when
+ * renaming triggers on a partitioned table.
+ */
+static void
+renametrig_partition(Relation tgrel, Oid partitionId, Oid parentTriggerOid,
+					 const char *newname)
+{
+	SysScanDesc	tgscan;
+	ScanKeyData	key;
+	HeapTuple	tuple;
+	int		found = 0 PG_USED_FOR_ASSERTS_ONLY;
+
+	/*
+	 * Given a relation and the OID of a trigger on parent relation, find the
+	 * corresponding trigger in the child and rename that trigger to the given
+	 * name.
+	 */
+	ScanKeyInit(&key,
+				Anum_pg_trigger_tgrelid,
+				BTEqualStrategyNumber, F_OIDEQ,
+				ObjectIdGetDatum(partitionId));
+	tgscan = systable_beginscan(tgrel, TriggerRelidNameIndexId, true,
+								NULL, 1, &key);
+	while (HeapTupleIsValid(tuple = systable_getnext(tgscan)))
+	{
+		Form_pg_trigger	tgform = (Form_pg_trigger) GETSTRUCT(tuple);
+		Relation		partitionRel;
+
+		if (tgform->tgparentid != parentTriggerOid)
+			continue;	/* not our trigger */
+
+		Assert(found++ <= 0);
+
+		partitionRel = table_open(partitionId, NoLock);
+
+		/* Rename the trigger on this partition */
+		renametrig_internal(tgrel, partitionRel, tuple, newname);
+
+		/* And if this relation is partitioned, recurse to its partitions */
+		if (partitionRel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
+		{
+			PartitionDesc	partdesc = RelationGetPartitionDesc(partitionRel, true);
+
+			for (int i = 0; i < partdesc->nparts; i++)
+			{
+				Oid		partitionId = partdesc->oids[i];
+
+				renametrig_partition(tgrel, partitionId, tgform->oid, newname);
+			}
+		}
+		table_close(partitionRel, NoLock);
+	}
+	systable_endscan(tgscan);
+}
 
 /*
  * EnableDisableTrigger()
diff --git a/src/backend/parser/gram.y b/src/backend/parser/gram.y
index 10da5c5c51..26433c529f 100644
--- a/src/backend/parser/gram.y
+++ b/src/backend/parser/gram.y
@@ -8886,7 +8886,7 @@ RenameStmt: ALTER AGGREGATE aggregate_with_argtypes RENAME TO name
 					n->missing_ok = false;
 					$$ = (Node *)n;
 				}
-			| ALTER TRIGGER name ON qualified_name RENAME TO name
+			| ALTER TRIGGER name ON relation_expr RENAME TO name
 				{
 					RenameStmt *n = makeNode(RenameStmt);
 					n->renameType = OBJECT_TRIGGER;
diff --git a/src/test/regress/expected/triggers.out b/src/test/regress/expected/triggers.out
index 5254447cf8..0380257aee 100644
--- a/src/test/regress/expected/triggers.out
+++ b/src/test/regress/expected/triggers.out
@@ -3410,3 +3410,122 @@ for each statement execute function trigger_function1();
 delete from convslot_test_parent;
 NOTICE:  trigger = bdt_trigger, old_table = (111,tutu), (311,tutu)
 drop table convslot_test_child, convslot_test_parent;
+--
+-- build a nested partition scheme for testing
+--
+create table grandparent (id int,
+primary key (id))
+partition by range (id);
+create table middle partition of grandparent for values from (1) to (10)
+partition by range (id);
+create table chi partition of middle for values from (1) to (5);
+create table cho partition of middle for values from (6) to (8);
+create function f () returns trigger as
+$$ begin return new; end; $$
+language plpgsql;
+create trigger a after insert on grandparent
+for each row execute procedure f();
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('a')
+order by tgname, tgrelid::regclass::text;
+   tgrelid   | tgname | parent_tgname 
+-------------+--------+---------------
+ chi         | a      | a
+ cho         | a      | a
+ grandparent | a      | 
+ middle      | a      | a
+(4 rows)
+
+alter trigger a on grandparent rename to b;
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('a', 'b')
+order by tgname, tgrelid::regclass::text;
+   tgrelid   | tgname | parent_tgname 
+-------------+--------+---------------
+ chi         | b      | b
+ cho         | b      | b
+ grandparent | b      | 
+ middle      | b      | b
+(4 rows)
+
+alter trigger b on only middle rename to something;
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('something', 'b')
+order by tgname, tgrelid::regclass::text;
+   tgrelid   |  tgname   | parent_tgname 
+-------------+-----------+---------------
+ chi         | b         | something
+ cho         | b         | something
+ grandparent | b         | 
+ middle      | something | b
+(4 rows)
+
+alter trigger something on middle rename to a_trigger;
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('a_trigger', 'b', 'something')
+order by tgname, tgrelid::regclass::text;
+   tgrelid   |  tgname   | parent_tgname 
+-------------+-----------+---------------
+ chi         | a_trigger | a_trigger
+ cho         | a_trigger | a_trigger
+ middle      | a_trigger | b
+ grandparent | b         | 
+(4 rows)
+
+--
+-- Check that classical inheritance is unphased by renaming triggers
+--
+create table inh (id int,
+primary key (id));
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgrelid = 'chi'::regclass
+order by tgname, tgrelid::regclass::text;
+ tgrelid |  tgname   | parent_tgname 
+---------+-----------+---------------
+ chi     | a_trigger | a_trigger
+(1 row)
+
+alter table middle detach partition chi;
+alter trigger a_trigger on middle rename to some_trigger;
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgrelid = 'chi'::regclass
+order by tgname, tgrelid::regclass::text;
+ tgrelid | tgname | parent_tgname 
+---------+--------+---------------
+(0 rows)
+
+alter table chi inherit inh;
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgrelid = 'chi'::regclass
+order by tgname, tgrelid::regclass::text;
+ tgrelid | tgname | parent_tgname 
+---------+--------+---------------
+(0 rows)
+
+create trigger unrelated before update of id on inh
+for each row execute procedure f();
+alter trigger unrelated on inh rename to some_trigger;
+alter trigger some_trigger on inh rename to trigger_name;
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('some_trigger', 'unrelated', 'trigger_name')
+order by tgname, tgrelid::regclass::text;
+ tgrelid |    tgname    | parent_tgname 
+---------+--------------+---------------
+ cho     | some_trigger | some_trigger
+ middle  | some_trigger | b
+ inh     | trigger_name | 
+(3 rows)
+
+-- cleanup
+drop table grandparent;
+drop table chi;
+drop table inh;
+drop function f();
diff --git a/src/test/regress/sql/triggers.sql b/src/test/regress/sql/triggers.sql
index 7b73ee20a1..5be330508e 100644
--- a/src/test/regress/sql/triggers.sql
+++ b/src/test/regress/sql/triggers.sql
@@ -2572,3 +2572,96 @@ for each statement execute function trigger_function1();
 delete from convslot_test_parent;
 
 drop table convslot_test_child, convslot_test_parent;
+
+--
+-- build a nested partition scheme for testing
+--
+create table grandparent (id int,
+primary key (id))
+partition by range (id);
+
+create table middle partition of grandparent for values from (1) to (10)
+partition by range (id);
+
+create table chi partition of middle for values from (1) to (5);
+create table cho partition of middle for values from (6) to (8);
+
+create function f () returns trigger as
+$$ begin return new; end; $$
+language plpgsql;
+
+create trigger a after insert on grandparent
+for each row execute procedure f();
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('a')
+order by tgname, tgrelid::regclass::text;
+
+alter trigger a on grandparent rename to b;
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('a', 'b')
+order by tgname, tgrelid::regclass::text;
+
+alter trigger b on only middle rename to something;
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('something', 'b')
+order by tgname, tgrelid::regclass::text;
+
+alter trigger something on middle rename to a_trigger;
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('a_trigger', 'b', 'something')
+order by tgname, tgrelid::regclass::text;
+
+--
+-- Check that classical inheritance is unphased by renaming triggers
+--
+
+create table inh (id int,
+primary key (id));
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgrelid = 'chi'::regclass
+order by tgname, tgrelid::regclass::text;
+
+alter table middle detach partition chi;
+
+alter trigger a_trigger on middle rename to some_trigger;
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgrelid = 'chi'::regclass
+order by tgname, tgrelid::regclass::text;
+
+alter table chi inherit inh;
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgrelid = 'chi'::regclass
+order by tgname, tgrelid::regclass::text;
+
+create trigger unrelated before update of id on inh
+for each row execute procedure f();
+
+alter trigger unrelated on inh rename to some_trigger;
+
+alter trigger some_trigger on inh rename to trigger_name;
+
+select tgrelid::regclass, tgname,
+(select tgname from pg_trigger tr where tr.oid = pg_trigger.tgparentid) parent_tgname
+from pg_trigger where tgname in ('some_trigger', 'unrelated', 'trigger_name')
+order by tgname, tgrelid::regclass::text;
+
+-- cleanup
+
+drop table grandparent;
+drop table chi;
+drop table inh;
+drop function f();

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