The wiki says this:
"but only where this is deemed to be too much of a slang name or
otherwise unofficial-sounding. Ordinarily though, the name which local
people use is the name we set in the name=* tag!"
https://wiki.openstreetmap.org/wiki/Names#Local_names_(loc_name)
This is, once again, poor quality tagging. It's far too subjective. I
mean, what determines the cut off point for a name being too "slangy"?
If it's not on a road sign or in a street gazetteer database then it's
almost certain not to have a name. If there's no recorded evidence & the
name used is purely word of mouth in the local area, then it should be
tagged using loc_name.
DaveF
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