Signature on work?

[monochromatic99]

Hey guys, I was planning to offer up my drawings in a gig. The short question is, is it all right to leave a signature on the drawings done for non-commercial use? I won’t sign the work that has been commissioned for commercial use, but not having a signature for drawings that the buyer doesn’t have full rights to seem like a recipe for art theft. I did hear that the buyer has ‘full rights’, but there are different licenses that should be paid extra for. I’m kinda confused.

Thank you for any answers!