I do not know if this is the information you want, but one of the elements returned by caller(0) includes the (fully qualified) name of the called subroutine. (It'll be package::__ANON__ for a code block).

And note that if you have the name of a subroutine, you don't need 'eval' to call it.

    my $name_of_sub = "foo";
    $name_of_sub->(...arguments...);
[download]

works, provided you turn off strict 'refs' when you call the subroutine.