With three different backgrounds there are essentially three different Vs to choose from. I don't think it would be at all unreasonable to expect the three of them to have different personalities and different ways of speaking. However what we end up getting feels more like a chimera of the three Vs. The main reason for this is most likely that CDPR didn't want to write and record three different sets of dialogue for V.Hey,
I think the concept of V is pretty good, but I don't like how (s)he quite literally changes personalities between quests based on hardcoded motives.
V's personality should be merc + selected background, but I feel like it ranges anywhere from being an explosive maniac to an empathetic listener.