Theodosia combines the Greek theos (God) and dosis (giving) — meaning "giving of God" or "gift of God." Theodosia Burr (1783-1813), the daughter of Aaron Burr, was the subject of the song "Dear Theodosia" in Hamilton.
Theodosia is rare but rising thanks to Hamilton.
Theodosia 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 Theodosia reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.