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"
"God is my judge (short form of Daniel)"
"son of Day, child of daylight"
"moonlight, lunar"
"the realization that every stranger has a full and vivid life"
"God has heard"
"victory of the people"
"reddish-brown color"
"hedged enclosure"
"sacred songs, hymns of praise"
"he to whom it belongs"
"from Saint Denis"
"hawthorn tree, thorny hedge enclosure"
"alder tree, from the grove"
"from the valley town"
"descendant of Ógán"
"resolute protector"
"to dwell, commander"
"heart's friend, chosen friend"
"son of the grey-haired one"
"from the island of Cyprus"
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.