Here is a little camlp4 code for an ad-hoc solution :
http://bluestorm.info/camlp4/Camlp4GenericProfiler.ml

It's based upon the Camlp4Filters/Camlp4Profiler.ml from the camlp4
distribution.
The GenericMake functor will traverse your code and apply the
parametrized function to the body of each function declaration. You
can use it with a functor providing a  (with_fun_name : string ->
Ast.expr -> Ast.expr), transforming the Ast to your liking, given the
function name.

I've written a small LoggingDecorator module that operates on the
__LOG__ identifier. Example code :
  let __LOG_FUNC__ func msg =  Printf.eprintf "in function %s: %s\n%!" func msg
  let test_function p = if not p then __LOG__ "p is false !"

It will replace the __LOG__ identifier with a __LOG_FUNC__ "p".

You can change that behavior, in particular you could be interested
(for logging purpose) in the location of the function declaration, not
only his name : see how the initial Camlp4Profiler behavior (wich i
kept in the ProfilingDecorator) do that (Loc.dump).