Ayumi sits next to 4 phonetic neighbors — Yumi, Ami, and Naomi are the closest matches by sound. Most share Ayumi's Japanese cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"walking, pace, progress"
"pleasure, delight"
"lady, mistress, respected woman"
"gift of God"
"flame, hill"
"meadow of the brave"
"pearl"
"From Saint-Denis, France"
"God will add; gracious"
"anointed one"
"noble kind, noble type"
"one who shows mercy"
"mystery, secret"
"elf ruler (alternative folk etymology)"
"sun and moon combined"
"fawn, young deer"
Similar sound: These names share phonetic patterns with Ayumi — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Japanese origins, giving them the same cultural heritage as Ayumi.
Rhythm: Ayumi is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.