Yeah, you can add a water bowl. Just make sure that he can comfortable sit up without his mouth being submersed. And yes, the "common pacman frog" is generally considered to be the Ceratophrys cranwelli, which is what your cute little guy is.

This looks like it's a decently setup starter tank (assuming it has a lid with holes to keep in humidity). It'll probably be a good idea to upgrade his tank size and add cocofiber as substrate once he gets a little bigger. Don't be afraid to ask any questions that you might have.