Asta is the Old Norse short form of Astrid — "divine beauty." Asta Gudbrandsdatter (c. 970-c. 1020) was the Norwegian noblewoman and mother of Saint Olaf II Haraldsson — the warrior-king who Christianized Norway and became its patron saint.
Asta Nielsen (1881-1972) was the iconic Danish silent-film star.
Asta 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 Asta reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.