Fyn sits next to 3 phonetic neighbors — Finn, Flynn, and Fin are the closest matches by sound. Most share Fyn's Irish-rooted cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"fair, white, bright"
"chaplain, keeper of the chapel"
"the essential point, heart of the matter"
"lord of the earth, creation of the good earth"
"son of Kay"
"unknown, possibly nickname"
"with great strength (via Arion)"
"friend, lover (of God)"
"ruler of the land"
"settlement on a hill"
"water farmstead"
"beloved strength"
"a legend, a tale"
"Farmer; earth worker"
Similar sound: These names share phonetic patterns with Fyn — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old Irish/Gaelic origins, giving them the same cultural heritage as Fyn.
Rhythm: Fyn is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.