It seemed to me like "The Dark Urge" was a title, not a name. Something to distinguish it from "Vanilla" Tav. I doubt you'll be introducing yourself to NPCs as The Dark Urge, as hilarious as that could be.
"Nice to meet you Gale, my name is The Dark Urge, but my friends just call me The Urge."
"Right then. Pleasure to meet you..."
This is what I'm hoping for, yeah. But in the stream that is the name 'The Dark Urge' goes by, even when introducing themselves....which IDK, maybe that's the default name (instead of Tav) and you can change it, or it's the one they chose for the stream? Either way, I don't quite fancy going by 'The Dark Urge' for a 160 hour playthrough.