I agree that a removal option would be better, sometimes old profiles become broken after updates, or better profiles are later created.
For now, one thing you can do if you still have the original file you uploaded, is to attempt to reshare it again, but first change its name to some garbage, like “…..”. That way it will not appear in searches for that game name. A trick I have used before, but admittedly need to do with several of my old profiles.