Dolly Levi is the title character of the Broadway musical "Hello Dolly!" She's a lively, independent, romantic and downright charming woman. In 1969, Barbra Streisand played Dolly Levi in the movie adaption.
Darya "Dolly" Schterbatskya was a character in Leo Tolstoy's "Anna Karenina". I think this name is a bad name, but a cute nickname that should stop being used once the child reaches age 8 or so.
Dolly was the name of the first cloned sheep and the first clone of an adult animal. The scientists named her after Dolly Parton. After her death, she was stuffed. You can see her in the Scottish National Museum.