People have read far more into what Jobs said, than what he actually said
Jobs simply said that a prototype touch tablet gave him the idea for the iPhone. He did not say that the same OS was involved at all.
In fact, according to various iPhone histories, we've been told that Apple didn't begin the mobile OSX port until early 2006. Before that, they had even considered using Linux for the phone.
As for the name, the one I see most as an abbreviation is "iPOS" for iPhone / iPad OS, although I can see why that would turn some people off.