Hi,
Yes you can tile over the old tub surround. When you buy the adhesive let the supplier know what you are tiling over so you can get the best adhesive for the job.
If you remove the old tub surround, you may find you can’t remove the remains of the old adhesive so you will end up having to replace that part of the wall.
DONT EVEN THINK ABOUT IT. Remove the old tub surround and any drywall behind it. Install 1/2 inch thick DUROC or similar cement board with special Duroc screws. Mess tape and mortar your joints. Now you are ready to tile.