Clayton sits next to 5 phonetic neighbors — Layton, Peyton, and Dayton are the closest matches by sound. Most share Clayton's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"gift of God"
"river"
"round, barrel-maker"
"first, chief"
"ruler of the army"
"eagle"
"rich friend, prosperous friend"
"Beauty, grace"
"God is gracious (via John/Zane)"
"black gemstone"
"ash tree town"
"son, born of"
"tall, imposing one"
"little fire"
"at the ash tree"
"tiller of the soil, agriculturalist"
"from Laurentum, laurel-crowned"
Similar sound: These names share phonetic patterns with Clayton — similar vowel sounds, consonant clusters, or rhythm.
Rhythm: Clayton is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.