The name Asta is a girl's name of Greek origin meaning "divine strength". Asta and is often added to lists like Unique Baby Names: Unusual and Rare and discussed in our forums with posts like "Quick Question Thread?!".
From the experts:
This Scandinavian name was made famous in English-speaking countries as the name of the dog in the "Thin Man" series. Danish actress Asta Nielsen was another famous bearer. Asta can be considered as a short form of Astrid or Augusta.