Apollonia is the Greek feminine of Apollonios — "of Apollo," the Greek god of light, music, and prophecy. Saint Apollonia of Alexandria (d. 249) was a 3rd-century virgin-martyr — patron saint of dentistry (her teeth were broken in martyrdom).
Apollonia Vitelli is the Sicilian first wife of Michael Corleone in The Godfather.
Apollonia 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 Apollonia reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.