Williams sits next to 3 phonetic neighbors — Wilson, Willis, and Williamson are the closest matches by sound. Most share Williams's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"resolute protector"
"son of Diot, follower of Dionysus"
"emperor, ruler, kingly"
"belonging to Christ"
"divine, godlike"
"of the moon, lunar"
"bard, poet (from Irish Daimhin)"
"passion, zeal (from root name Rhys)"
"wave"
"may God protect"
"servant, attendant"
"spirit, vigorous enthusiasm, flair"
"lover of the earth"
"Yahweh is my power"
"heart"
"dedicated to Mars"
"free ruler, powerful peace"
"of the Dorians"
"settlement on a Roman road, farm on the paved way"
"victory, honor"
"eastern town"
Similar sound: These names share phonetic patterns with Williams — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Germanic origins, giving them the same cultural heritage as Williams.
Rhythm: Williams is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.