Case sits next to 4 phonetic neighbors — Chase, Ace, and Casey are the closest matches by sound. Most share Case's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"maker of cases or boxes"
"son of Walter"
"dweller by the woods"
"powerful ruler"
"ruler, sovereign (from Julius Caesar's name)"
"little cloak, beloved"
"Hugh's settlement, town"
"consecrated, increased"
"descendant of the sun god"
"dark-haired, tawny"
"ever awake"
"God is gracious (via John → Jack)"
"long stone settlement"
"path, track, trail"
"God has remembered"
"the greatest"
"son of the wealthy guardian"
"son of the south"
"companion, fellow traveler"
"gift of God"
"fair-haired one"
Similar sound: These names share phonetic patterns with Case — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old French casse/Latin capsa origins, giving them the same cultural heritage as Case.
Rhythm: Case is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.