Rufus sits next to 4 phonetic neighbors — Rufous, Remus, and Cletus are the closest matches by sound. Most share Rufus's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"red-haired, auburn-haired"
"son of Dionysus"
"from Ludwig/Louis (via Swedish)"
"top of the steep place"
"elegant"
"beloved of Yahweh"
"peaceful, tranquil"
"eager enthusiasm"
"from the ash tree valley"
"friend of God"
"iron blazing, battle warrior"
"peace, repose"
"wise counsel and army"
"God heals, God supports"
"hollow stone, hollow hill"
"valley, dell"
"brave warrior (via Wyatt)"
"rejoice, be happy"
"worker, one who builds"
"helped by God, God has supported"
"possessor of goodness, kingly"
Similar sound: These names share phonetic patterns with Rufus — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Latin origins, giving them the same cultural heritage as Rufus.
Rhythm: Rufus is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.