Clarence sits next to 5 phonetic neighbors — Clara, Clarice, and Florence are the closest matches by sound. Most share Clarence's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"bright, clear, famous"
"God will add, God increases"
"beautiful one"
"from Leicester; possibly heavenly"
"to soothe, to comfort"
"bright like a bear"
"of the Claudian family"
"meadow on a ledge"
"shining, celestial light"
"short form of Lavinia"
"prosperous friend"
"settlement of the Britons"
"washed, cleansed; or variant of Lavinia"
"flowing, moving freely"
Similar sound: These names share phonetic patterns with Clarence — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Latin origins, giving them the same cultural heritage as Clarence.
Rhythm: Clarence is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.