Amethyst sits next to 3 phonetic neighbors — Amelia, Amber, and Amara are the closest matches by sound. Most share Amethyst's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"purple gemstone"
"beam of light (modern association)"
"place of worship, sacred place"
"princess, female commander"
"slender, noble"
"shining, bright"
"renowned warrior"
"supplanter, held by the heel"
"beautiful"
"from the marshes"
"sparkling, bright as crystal"
"anointed one"
"torch of light (from Eleanor)"
"sun (via Persian Kira)"
"my God is abundance"
"modern invented name"
"pearl (short form of Margaret)"
"victory of the people (via Colin/Nicholas)"
"child of the earth"
"forever blooming"
"bird"
Similar sound: These names share phonetic patterns with Amethyst — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Latin origins, giving them the same cultural heritage as Amethyst.
Rhythm: Amethyst is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.