Hyrum sits next to 4 phonetic neighbors — Hiram, Cyrus, and Tyrus are the closest matches by sound. Most share Hyrum's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"exalted brother, my brother is high"
"huntsman, game warden"
"sky god, shining deity"
"bard, poet (from Irish Daimhin)"
"settlement at the clean/pure place"
"noble, warrior, of high birth"
"of the trees"
"thank you, grateful"
"son of Hudde (son of Hugh)"
"three (numeric)"
"modern coined name, Z + sound"
"from Wynstan's estate"
"of the crow, raven-haired"
"God is gracious (from Shawn/Sean)"
"healer"
"settlement by a church, church village"
"blooming, flourishing"
"the best, highest card"
"hazel tree"
"to conquer"
"dark complexion"
Similar sound: These names share phonetic patterns with Hyrum — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Hebrew origins, giving them the same cultural heritage as Hyrum.
Rhythm: Hyrum is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.