Graeme sits next to 4 phonetic neighbors — Graham, Grey, and Grayham are the closest matches by sound. Most share Graeme's Scottish cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"grey home, gravelly homestead"
"rejoice, be glad (via Gaius/Caio)"
"reflected sound"
"one who cuts, cutter of cloth or stone"
"settlement of Leaxa's people"
"marshland meadow"
"brother (informal)"
"fire brand, flaming sword"
"imperial authority"
"precious gem, jewel"
"split, torn apart"
"place of the elms"
"child born at a prosperous time"
"foot soldier"
"sky blue, cerulean"
"gracious, merciful"
"related to Everett (brave boar)"
"son of Aodh (fire)"
"first of the month, calends"
"little king"
Similar sound: These names share phonetic patterns with Graeme — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old English origins, giving them the same cultural heritage as Graeme.
Rhythm: Graeme is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.