Amyri sits next to 4 phonetic neighbors — Amira, Amari, and Emery are the closest matches by sound. Most share Amyri's Arabic-inspired-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"princess, commander"
"princess"
"boomerang, returning stick"
"graceful, free-spirited"
"western pool or stream"
"light brown, golden"
"gift freely given by the gods"
"lovable, dear"
"each of the two (variant etymology)"
"oak tree"
"beautiful, lovely"
"son of the gray-haired one"
"faith, faithfulness"
"friend, beloved"
"herb garden estate"
"gift of Yahweh"
"orchid flower"
"life"
"servant of God"
"life (from Zoe) with feminine diminutive"
"orchid flower"
Similar sound: These names share phonetic patterns with Amyri — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Arabic-inspired origins, giving them the same cultural heritage as Amyri.
Rhythm: Amyri is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.