The Relic is using data that's on the engram (the neural network, i.e., memories and personality) to brainwash (overwrite) V's consciousness into believing they are Johnny.
And it doesn't make a new consciousness because consciousness is strictly a local, tied to one's unique physical brain, perception of reality. So in order to make one, the Relic would need to create a new biological brain, which it clearly doesn't.
Johnny is not a separate entity. He is just a part of V's brain and consciousness. When they both talk, they are not actually talking -it's just V's brain trying to make sense of having two personalities. This further proves the point when Hellman says: "What's it like to have two personalities?" and "You're not actually "talking," but yes, I understand what you mean."
She appears to be conscious, but she isn't, though. Well, maybe, somehow in her own way, but definitely not in a way a physical human brain can be.
they imply the relic is actually creating a new "brain" vik says its destroying his brain cells, and built new brain matter where damage was. and hellman says his brain can no longer survive without the relics neurology (when you meet him at Kang tao)
I had assumed the relic was a more simple system, but apparently the nanites are creating neural tissue and taking over. The chip is a biochip BTW, not just a piece of tech.
So, if relic 2.0 is creating a local brain to match the engram, would you consider that to be a new consciousness