It seems that Haskell has established several naming conventions around monads.
Examples:
T to the end to obtain the name of the mon
runX m where m :: X a will run the X monad and return the "side effect" along with the monad result, a.
evalX m will run the computation and return the result, a.
execX m will run the computation and return the "side effect" but not the result.
The lifts come in various flavors that can be a bit too tricky for me to want to explain them in a SO answer. You should probably know lift and liftIO and be aware of / eventually seek out the other variants such as liftWith and liftBaseWith. See, for example, EZYang's posting on the topic.
appending a T after the monad name implies transformer. Appending an M after a function name implies it is monadic. Appending an _ implies the result is ignored.
All other suffixed letters mean "use hoogle".