Are you referring to an iOS-OS X merger or a rename of just OS X? Either way, I find it highly unlikely.
While OS X and iOS are separate, "Apple OS" could mean either one. OS X and iOS are already widely recognized names, so it is also unlikely for this reason.
A merged "iOS X" is unlikely because each OS is designed for specific types of usage, hardware, and methods of input. It isn't going to happen anytime soon.
They won't. You're not running the same software on your iPad as you are your Mac, so why are we going to refer to it as if we are? Obviously if it's an Apple product, it's running an Apple produced OS too.