I do this on WoD games to an extent. I rarely ever port a character over wholecloth. I usually keep the name, PB, and general feel of a character and then adjust the character to the new setting.
I do this for a few reasons, one, the themes on WoD games generally don't vary enough to make it impossible.
Two, WoD games have such a short lifespan that I generally don't get to play out a complete character arc to my satisfaction. The only way for me to get to the point where I feel like I'm done with a character is to play out their arc over several games. Generally, my starting point on what game is a few ticks advanced on from my starting point on the previous game.
Three, Because WoD games are so short-lived I sometimes don't want to waste effort on a completely new concept until I know the game's going to be active for longer than a month.
Four, Sometimes, I think a concept is going to work on a game and it just ... doesn't, so I shelve the concept and try again on a new game.
For example, with Natalie over on echoes is a recycle of Natalie on SF. SF-Natalie was raised in a ghoul-family. The killing of the family's regnant left them mostly to their own devices. So Natalie poked at the supernatural until she got noticed and ghouled. Echoes-Natalie is one tick along the story was raised in a ghoul family with the intention that she'd always take over and be ghouled. Like SF-Natalie, Echoes-Natalie dabbled with mortal groups exploring the supernatural, but while SF-Natalie did so exploring her own family secrets, Echoes-Natalie did so in preparation for service. With both, there was a period of time that they were free of vampiric influence, but with Echoes-Natalie the choice to become a ghoul was her own, made as the best possible way to increase her family's influence. She is now utterly devoted to her regnant, though with some nagging regrets. Both characters have the same, smooth, polished demeanor and likely will interact with PCs similarly, and both have a family business that they're shepherding.
With Echoes-Natalie, I was excited about having the char play a 'bridge' and be more involved in the mortal sphere than vampiric sphere, however at this point in the game, I very much doubt that is going to happen, so I'll likely shelve that idea and bring out a form of Natalie again on a future game where I think I might be able to accomplish that bridge concept again, or I may come up with a better idea for making a mortal-vampiric bridge character and run with that instead.