Phoenix sits next to 3 phonetic neighbors — Felix, Phineas, and Lennox are the closest matches by sound. Most share Phoenix's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"dark red, crimson"
"occupational name for an archer or bowman"
"kingly"
"God is gracious"
"chosen savior"
"son of Kyle"
"son of the home ruler"
"man, mankind, human"
"one who mills grain"
"enthusiasm, passion"
"ruler of the elves"
"son of Brice"
"son of Carsun, dweller near the marsh"
"meadow dwelling, water meadow"
"valley dweller"
"dispenser of provisions, household steward"
"promised land, sanctuary"
"one who is learned"
"Gift from God"
"at the ford"
Similar sound: These names share phonetic patterns with Phoenix — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Greek origins, giving them the same cultural heritage as Phoenix.
Rhythm: Phoenix is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.