Kaius sits next to 4 phonetic neighbors — Caius, Kai, and Darius are the closest matches by sound. Most share Kaius's Latin-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"rejoice, be glad"
"free man"
"wise as a wolf"
"anointed one"
"coal farm"
"warrior"
"God has given"
"conqueror, victor"
"all wise (from Norse Alviss)"
"difficult journey"
"valley dweller, from the valley"
"peace"
"olive tree"
"gift of God, gift of Yahweh"
"army ruler, power of the army"
"rest, comfort (when used as variant of Noah)"
"divine reward (alternate interpretation)"
"Basque masculine name, nature-connected"
Similar sound: These names share phonetic patterns with Kaius — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Latin origins, giving them the same cultural heritage as Kaius.
Rhythm: Kaius is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.