Here's my wild guess:
The AVR parts aren't going to be renamed/renumbered. Or if I'm wrong and they are being renumbered, it isn't going to be as drastic as renaming them into the PIC family. (amyk's suggestion of a AVR prefix makes sense - maybe something like AVR32U4).
Existing ARM parts will likely not be renumbered. New parts will be added as something like PIC32CX (CX=cortex).
I'm not aware of an instance where microchip has ever renumbered a product after acquisition - at least not with any of their recent acquisitions. I'm guessing there might have been cases that I'm not aware of, but at least for those parts I'm aware of, parts have not been renumbered. In many cases, followon products have also followed the pre-acquisition numbering scheme for that family. I.E. there are new "Roving Networks" modules - microchip seems to be using the RN prefix for roving-style modules, even if they are a new design.