Although they would work in this case, since it is also possible for folder and filenames to contain dots other than the extension separator, none of the suggestions so far should be considered as general solutions to removing the extension from a file name.
The safest way to do this is a variation in Doc's code using InStrRev() to locate the last dot.
Developers should not be excessively focused on simplification of the appearance of the code. The simplest code is not always the most efficient code. Although I have not tested, I would expect Split() to have significant overheads., though it probably doesn't really matter much.
The desire for simple looking code often drives developers to overuse user-defined-functions when the job can be done with native SQL engine functions that, although they look more complex in the SQL, will perform better than a UDF.