This is an active area of research! I studied the was the early Shazam algorithm worked, and unfortunately, you wouldn't be able to recognize voice actors using the same algorithm. Here's why:

The Shazam algorithm is really a search: you give it the input, it says, "oh, I've heard that exact same section in this song!" and it tells you the name of the song.

Recognizing something your system has never seen before is a little bit different: you'd want an algorithm that says, "well, I haven't ever heard these words before, but given [list of qualities about the audio] I'm fairly certain it's [voice actor]."

Image you're looking for a face, but you've only got a picture of the nose. The Shazam algorithm will say, "I've seen this nose before, so I'll try to line up the nose on every single picture I have until it's a perfect match".

Your algorithm would be, "well, I've never seen this nose before, but given my other pictures, who is it most likely to belong to?" You're never going to get a perfect match, but you can look at other qualities the pictures to try to make the best guess.

Edit: of course the algorithms are more complicated than that, but that should give you the jist