Phoenix is from the Greek phoinix ("crimson, purple") — the immortal bird that cyclically dies in flames and is reborn from the ashes, found in Egyptian (Bennu), Greek, Roman, Persian (Simurgh), Chinese (Fenghuang), and Slavic mythology. Phoenix Suns — NBA franchise since 1968.
Phoenix does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Phoenix reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.