ChordNames should (probably) drop/consume/merge extra octave bass notes before 
computing the structure of a chord. Unless I'm misunderstanding the source of 
the error.

The first name is correct. The extra bass note, even though it doesn't change 
the chord, confuses the chord computer. The 8 and 15 are both octaves and so 
shouldn't be included in the chord name.

\version "2.22.1"
\new ChordNames {
    <e c' e a>1
    <e, e' c' e a>1
  }
\new Staff \relative c'{
    <e c' e a>1
    <e, e' c' e a>1
}

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