<p>In an actionscript function (method) I have access to arguments.caller which returns a Function object but I can't find out the name of the function represented by this Function object. 
Its toString() simply returns [Function] and I can't find any other useful accessors that give me that...
Help :-/</p>

A function is just an object like any other - it doesn't have a "name" in and of itself; it only has a name in the sense that you might make one or more references to it. If what you're asking is how to get the name of the reference by which the function was called, then there's no general way to do that. (After all the function could be declared anonymously, in which case it has no name at all.)
It would probably be best to examine why you need to know the function's name, and figure out some other way to pass in or access the information you're trying to derive from that name. Passing in an additional parameter might be one approach, but it depends on what you're doing.