I've resisted responding to this because I hoped there would be some resolution in the recent Osgood releases, but no dice. I absolutely hate the idea of combining three distinct characters on the same page. However, I will begrudgingly accept it because I don't think we will ever get an answer on who actually died in Dark Water and then add to that, Osgood has now become a "position" that others like Bonnie can claim.
But Petronella? The fact that the Doctor says his name is Basil and Osgood later calls him Basil makes me very suspicious about whether she was serious about that being her name or not. Does Extinction confirm her first name is Petronella in-story?