Does the name on the new account have to be the same as on the old one? For example, could I let a friend use one of my old PSNs to enroll? It's convenient since with-PSN codes seem to allow "bill me later" rather than requiring a credit card up front.

Yes, that would work. It is currently unknown if sharing PSNs might have negative reprocussions for the "donor," so sharing isn't advised. Instead, use code 42m, which doesn't require a PSN, gives 7:2 with the 7th at 9.95, and has a bill me later option.