Gay sits next to 4 phonetic neighbors — Faye, Mae, and Ray are the closest matches by sound. Most share Gay's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"joyful, merry, carefree"
"land of the Bamar people"
"blind"
"little flower"
"nourishing, kind"
"from the island of Thera"
"excellent, outstanding"
"Dweller at the marsh"
"resolute protector"
"kola nut, sacred plant"
"moon"
"pure"
"well-born, noble"
"of the sorrows (religious title)"
"Bright fame; from Germanic elements hrod (fame) and possibly relate..."
Similar sound: These names share phonetic patterns with Gay — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old French (gai) origins, giving them the same cultural heritage as Gay.
Rhythm: Gay is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.