Take my name off the one bill. He have right to do that?

There's probably no way that you can get the bill from the phone company.

If you know that he's having an affair, maybe it's time to talk to a divorce lawyer.  One place to look for qualified attorneys is our website, http://attorneypages.com

Once you have a divorce action in progress, it's very possible that you can force him to turn over the phone records, or get them from the phone company, as part of the pre-trial discovery process.  It's a fairly simple thing for an experienced attorney.  You will probably need proof of something more than cell phone calls to prove adultery.  But even without that, there are usually other grounds for divorce, in a case like this, that will work.