Johnny.
Reason (spoilers): per Relic 2.0 documentation shard's in-game text (from Hellman), Relic 2.0 (which V has slotted in) can only activate construct transfer in the event of complete and _irreversible_ cease of any and all neural activity in the host body. I.e., the only way Johnny could even start taking over V's body - is if V's person would be entirely gone with no way to bring it back to life.
This means, with complete certainty, that V, as a person, is completely gone and dead shortly after Dex shoots V in the head. Certainly by the time construct 1st takes control of V's body motor functions - namely when Johnny (no more V!) repeatedly hits V's appartment wall with his forehead.
Consequently, it is all Johnny after that: he _imagines_ that V is alive, he pretends as if it's (by then actually gone) V's person who is controlling V's body (most of the time), he's having heavy case of split personality disorder (one person in his new 'ganic mind being "old Johnny", the other being "what Johnny thinks V would be"), and he's having hallucinations of his former self.
I.e., for most of the game, not only we play not as some mercenary (V), but as a ressurected terrorist, addict and murderer (Johnny) - he's also a psycho who thinks he's two people, while being just one.
"Bleh".