Is Apple ID the publisher name for apps or books created with iBooks Author?
No - when you actually sign up with iTunes connect to sell (or distribute for free) a podcast, music track, iBook, iOS app or Mac app - you enter into a much more formal relationship with Apple.

The forms are fairly self-explanatory and allow for you to specify the name of the business in a separate form that the name of the person filling out the form on behalf of the business. Of course, you can sell things in your own name and enter the same information in multiple places (which isn't what you are asking, but it's possible in general).

As with any contract, lawyers and accountants are advisable if you wish to know the costs and advantages of doing something personally versus as a business or corporation. That's far above our scope here, but in your case, iBooks Author will guide you through this sign up process. I have had 4 acquaintances sign up and all of them completed the initial sign up process in less than an hour. One decided to not use their personal account and is in the process of forming an LLC to sell books, but the others are intending to sell under their real names.

At worst, you will have signed up and wasted time and can just close your account and open another if you determine you didn't do it correctly or can't change some critical piece of information. I've seen plenty of app developers change their selling names and presume it was without signing up again, but once you sign up, you will have Apple to field questions on how to use their service and modify certain information you submitted if it needs to change.