While I still suspect that McGee's name change petition was an effort at crisis management, it seems to be a fairly clueless one.
First, if the problem is that his given name is not McGee, it may not have been necessary to actually file a name change petition. While Wisconsin has a statute that sets forth a process to change one's name by going to court, it is not the only way to change your name. Our Supreme Court has made clear that Wisconsin recognizes common law name changes which are accomplished by nothing more than "consistent and continuous use" of the new name as long as it is not done for fraudulent purposes. So if he's always been McGee and didn't become McGee to defraud someone (the voters?), he didn't need to do this.
Maybe the problem is that he is not always McGee. Jed at Boots and Sabers says that a quick public records check shows no driver's license issue to a Michael I. McGee, but that there is a driver's license issued to a Michael I. Jackson who is of the proper age (although who can really know what that should be?). But if he the problem is that he uses multiple names, when is he not McGee and why?
Maybe he is thoroughly McGee, but was just trying to err on the side of caution by filing a court petition. But, if so, why did he react the way he did to inquiries from reporters? At first, he said it was not a big deal and he'd discuss it later. Then he seemingly tried to disassociate himself from the petition as if he was laying the groundwork to abandon it. It's almost as if he decided it wasn't a good idea after he considered the implications of public disclosure.
But he couldn't have thought that he'd avoid public disclosure. He's a politician who certainly knew that he'd be recognized when he went to court. Besides, this statutory process requires that he publish a notice of the petition (which, if he did it correctly, should have already happened). And if the thing was done in response to a revelation that he is not McGee (because a scorned woman is about to out him or as a result of paternity testing?), the whole stupid idea was presumably to have a trump card that he could waive around claiming that, yes, he is McGee.
Or maybe he is McGee and found out his birth certificate is incorrect (when he said he didn't "have one", I suspect he meant it wasn't currently in his hands), but then why all the dissembling?
The bottom line, once again, is that McGee/Jackson is just a guy whose bulb shines dimly and whose default mode is hostility. Trying to figure out what someone else is up to is helped by the presumption that people act rationally. That presumption may not be applicable here.