Honestly, depends who the artist is and how you're using the work. Prime example is the Neo-Nazi Stonetoss, all the parodies and reworkings of his memes have the name removed or parodied to mock him.

If you're just taking a random persons artwork, then its probably best to leave the signature and credit them.

I think it's fine to leave the name as long as the edit makes it clear that the image has been edited.

Alternatively, add "Original by" above / in front of the signature.

I think editing the original artist's signature just like you edit the piece itself, could be a cool touch. That way you indirectly 'refer' to the original artist but also make it clear that you're not them. You can kinda play that artist's communist alter ego that way.