Also known as code switching. Many people do this all the time in the real world. I know black folk who have two distinct accents depending on the context and audience. Same with many southerners that I know. The drawl becomes a lot less pronounced in "professional" settings. That being said, V didn't grow up with Jackie. They met on a run. Corpo V might have grown up on the street as well, but then it's not really a different backstory.
Corpo V never did runs with Jackie before the game. In the Heros sidequest Mama Wells references that they lived under the same roof, though in retrospect that could be referencing the time skip at the beginning.
