Hays sits next to 3 phonetic neighbors — Hayes, Haze, and Maze are the closest matches by sound. Most share Hays's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"hedged enclosure"
"from the hare's den"
"flowing"
"divine wonder"
"manly, brave, strong (via Andre/Andreas)"
"known by God"
"peace, repose"
"song sung to a harp"
"dwelling near the church"
"bright will, shining desire"
"rejoice, be happy"
"strengthened by God"
"he enlightens, God enlightens"
"the fast one, arrow"
"of the night"
"battle, spirit of battle"
"tall, long-legged"
"young, youthful"
"creative elaboration of Jason"
"one from the sea"
Similar sound: These names share phonetic patterns with Hays — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old English origins, giving them the same cultural heritage as Hays.
Rhythm: Hays is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.