Hayk sits next to 4 phonetic neighbors — Hike, Jake, and Huck are the closest matches by sound. Most share Hayk's Armenian legendary history-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"eponym and patriarch of the Armenian people"
"God is gracious"
"God establishes"
"the sea belongs to God"
"disciple, devoted follower"
"distinguished, brilliant"
"vigilant in war (via Casey)"
"beginning, origin, creation"
"saint, holy one"
"belonging to the Lord"
"prince, commander, ruler"
"flowing water, river"
"modern invented name, variant of Cole/Colson"
"of the Cassius family"
"servant of the Most Merciful (Allah)"
"luxurious softness"
"may He add (referring to God)"
"son of Thomas, son of the twin"
"of Rudolf Diesel; fuel-powered engine"
Similar sound: These names share phonetic patterns with Hayk — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Armenian legendary history origins, giving them the same cultural heritage as Hayk.
Rhythm: Hayk is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.