Cai sits next to 4 phonetic neighbors — Kai, Kay, and Cay are the closest matches by sound. Most share Cai's Welsh cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"rejoice, delight"
"victors garland"
"boar-friend, warrior companion"
"pierce the valley"
"to flow, the descending river"
"thorny shrub, wild rose"
"hard, unyielding"
"from the hazel tree settlement"
"little hawk"
"one who serves"
"youthful, downy-bearded (first beard)"
"lord, master"
"man, husband (archaic)"
"small forest, wooded grove"
"the fifth"
"bald, little bald one"
"elf ruler"
"page boy, herald"
"from the bailey (castle wall)"
"muddy farm or settlement"
Similar sound: These names share phonetic patterns with Cai — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Latin via Welsh origins, giving them the same cultural heritage as Cai.
Rhythm: Cai is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.