Should I list my company as the publishing company, or my client’s?

This boils down to your comfort level and your client’s comfort level. If your client doesn’t want people to know where they got their book published for some reason or wants to take 100% credit, then that’s fine if that’s a service you offer. If a client’s provided materials seem a bit dodgy and you aren’t sure that they own the copyright or you aren’t sure if the material they’re providing is any good, you may not want to take that client on at all, but if you do you probably won’t want your name associated with it.

Generally speaking, I just list myself as the publisher on the copyright page and don’t get into things much deeper than that unless there’s a reason.