Rayme sits next to 5 phonetic neighbors — Remy, Raimi, and Ramona are the closest matches by sound. Most share Rayme's Germanic (via Raymond)-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"wise protector"
"Eagle power; noble strength"
"stony ridge, rocky heights"
"fierce valor, unlucky"
"Beautiful, lovely"
"people power"
"powerful ruler of ancestral lands"
"plume, ridge"
"God is gracious (through Juana/Juan root)"
Similar sound: These names share phonetic patterns with Rayme — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Germanic (via Raymond) origins, giving them the same cultural heritage as Rayme.
Rhythm: Rayme is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.