What is the proper name for when you change views or screens?
I have always called this a view / screen transition. This seems to be an accepted term across a variety of contexts, ranging from game development to software development, both through documentation and physical demonstration.
This term does not just cover the fact that we are moving from one screen or view to the other, but may also include additional effects that take place, during the process. For example, you might refer to a "fade-out" effect as one such transition.
I'd like to have decent terminology, because terminology affects all my variables, and changing it later is a pain
It sounds like your not properly documenting your code. It helps to use more universally accepted names, but consider that correct use of commenting should override any minor inconsistencies caused by incorrect name use.
The few languages I have used enforce this as a standard. In C#, for example, you can use ///<summary> </summary> above a variable to add a written summary of the variable as it should appear in documentation. This would more carefully explain the purpose of the variable to user's in cases where your name is not clear enough.
It is also worth considering the potential folly in assuming the level of understanding in others. The fact that such a term is universally accepted does not mean that every body who reads your code will take the same understanding.
I think it may be called "screen", but my games are not full screen, so I am not sure if that makes sense
In this context, you seem to be describing the actual game screen, as opposed to movement between game screens. Screen seems perfectly fine, here. Consider this: if "screen" meant "full screen", why would you need to make effort to say that your game is not "full screen"?
When I think of a "screen", in regards to games, I think of the area of the screen where the game is being drawn, and the context. If I had two separate games running, side by side, I would refer to them as separate game screens. If I moved from one menu to another, in either game, I would refer to it as changing menu screens.
If this term still feels awkward, to you, you might consider "viewport". A viewport is the space your game camera draws to; in most contexts, this is your game screen. Some games may involve multiple cameras, that each use a different viewport. Split screen multiplayer is one such example.
