It is called a shower valve. Many brands are available. Delta and Moen are among the favortites. Do not go real cheap, because you do not want to do this again!
The best way is to cut an access from the bedroom side. That is much easier to patch than the fibreglass/
The valve may be soldered in place, and the new one may need to be soldered as well.
I would recommend that you replace your 2 handle unit with a single handle pressure balanced or thermostatic unit. Chrome trim plates are available ( "Smitty Plates") to trim out the 2 holes in your fibreglass.
Now, shower valves are usually repairable, so before jumping into this project , it may be worthwhile to have a plumber look at it. Of course, if you just want to go all new, that's fine also.