Musa (MOO-zah) means "muse" in Italian and is a very rare feminine name. In the animated series "Winx Club" created and directed by Italian animator Iginio Straffi there is a feminine character called Musa. Here Musa is both linked with muses but also a wordplay with the Italian word musica meaning "music".
I knew this was a male name and a variant of Moses (Musa from Winx Club not withstanding), but in researching into Soviet Russian ballet in the 1950s I found a Russian (? She was dancing in Russia) ballerina by the name of Musa Gottlieb. I also saw it spelled Muza. She is pretty much nonexistent on the Internet, the only thing that can be found is that she was in the film ‘Stars of the Russian Ballet', but she was dancing opposite a famous dancer so I would assume she had some kind of career, and yet there is nothing, at least on the English internet. Hm...
Musa is also used in Chechnya (a traditionally Islamic country) as a first name for men. Since Chechnya is forced to follow the Russian naming system, it is also found as a middle name in the form of a patronymic, namely Musayevich (which would be Musa-khant in proper Chechen).