Is it possible in Haskell to implement a function which returns its own function name?
A possible type could be (a -> b) -> String.
You can preprocess your source code with CPP. In CPP
#define _NAMEOF(name) #name
defines a macro, _NAMEOF, for stringifying text (including surrounding it with programmer's quotation marks). You can then use it as follows:
head [] = error $ _NAMEOF(head) ++ ": empty list!"
which CPP should translate into a valid Haskell source code line:
head [] = error $ "head" ++ ": empty list!"