13-year-old Black just gave an interview to the AP -- in which the singer says she desperately wants a career as a respected recording artist ... adding, "I don't want to be known as the `Friday' girl. Hopefully, I can be known as Rebecca Black and not the `Friday' girl."
Black -- whose smash hit has landed more than 118 million views on YouTube -- added, "I want to be a performing artist. That's what I've always wanted to do."
For the record -- Black recently locked down a 5-song album deal ... which means she's already light years ahead of the "Chocolate Rain" guy.