replacementshower
Not really sure what kind of handle this is or how to replace it. It doesn't work anymore so no water comes out of the showerhead. There's some little pin in the base of the handle that broke and none of the hardware stores around here have any replacement parts for it. I'd really like to remove and replace it with something more modern.
That diameter would be very close to a M2.5 at 1.993mm minor screw. A hex head cap screw (AKA Allen head) could replace the Phillips.
Its also a bit smaller than an ANSI #4-40 at .0805inch minor
You could try the approximate size and get the matching tap for the closest interference fit.
That's definitely a Moen. It has a "pull out dial" handle or (more specifically) Moen 96797 Chateau One-Handle Tub and Shower Knob; and I think the cartridge is 1225B.
Here's a video about replacing the cartridge (it shows exactly the save valve) and in the beginning you can see the tear drop shaped handle.
Best Answer
If you can't find matching parts, you will need to open up the wall and get a new shower diverter. You might be able to do it without damaging the tile if you approach it from the other side of the wall. You can do the work with push fittings and it will be relatively simple that way.