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"
"hay valley"
"messiah"
"one who follows at the heel"
"from the place of Einion"
"grey valley or settlement"
"one who tends a gate or hatchway"
"little rock, little stone"
"lucky, fortunate"
"defender of men"
"foreigner, of the Welsh"
"estate by the cliff"
"descendant of fire, young warrior"
"realm of the dead"
"keen ruler, bold king"
"mountain of strength, exalted"
"bold journey, brave traveler"
"precious gem, jewel"
"the Lord is salvation"
"hospitable"
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.