[scintill76]

Similar here. I too have used my CC for refills and may have given my name for caller ID purposes, but I don't think it was mandatory nor do they have my SSN or other hard details on my identity.

AFAIK you shouldn't have to get a throwaway phone either. "SIM Card Kit" or "Bring your own phone/device" may be keywords to research -- you should be able to get a SIM that you can put in any GSM phone, and it will come with instructions about a website to visit, or phone number to call, to activate it. If they insist on names etc and it's prepaid, you could give a fake name since it will have no bearing on your ability to use it, although I'd be worried that it might be illegal for some stupid reason.