You usually only have to provide CC details for verification purposes. Its not usually then billed by card, or linked to you in any way that matters.
Only the phone company know the phone belongs to you.
Basically unless you are doing illegal stuff it really shouldn't matter.
I have a punting phone on tmobile that i registered for adult content years back. Because its pay as you go, theres no bills or anything linking me to the phone that anyone who doesnt have my online password would see. If i was organising a terrorist plot, or kiddie porn ring, then it might be an issue as the govt could easily link me to the phone, but as I am doing nothing nefarious with it, its all good.