Traditional function overloading in a language like, say, C++, is provided so that a different function can be called depending on the parameter list signature. C++ has a formal parameter list for its fuctions, Perl does not so it is not part of its culture. You might like to consider if it is wise to try to bring a culture from one language into another.
Personally I have never been convinced about the advisability of function overloading, my view is that if you need different functionality then you should call a different function.