Unlike e.g. array refs, every code ref has a backreference to its glob (so that when you call it, caller can know the sub name). This is fairly easily accessible with the B module (which provides introspection facilities for perl thingies):

use B;
sub coderef2name {
   eval {
      my $obj = B::svref_2object( shift() );
      $obj->GV->STASH->NAME . "::" . $obj->GV->NAME;
   } || undef;
}
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Returns something like pkgname::__ANON__ for anonymous subs, or undef if something goes wrong (like being passed an array ref instead of a code ref).

Updated to use GV->STASH->NAME, not STASH->NAME. Thanks, betterworld

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