If the blues singer published her music under the name Lady A, and it wasn't just a nickname, she might be able to claim a trademark violation. If the blues singer did not bother registering her performance name as a trademark, she would have to prove there were no other Lady A's performing music, and might be required to show that she legally tried to protect her performance name before.

I doubt she would win, Lady A is so generic that there could be hundreds of singers with a first or last name using that moniker.