You can simply turn on the Deparse option of Data::Dumper:

use Data::Dumper;

sub a {
    print "abc";
}

sub b {
    print "123"
}

$hash = {"a",\&a, "b", \&b};
$Data::Dumper::Deparse = 1;
print Dumper($hash);
[download]

It also works with anonymous:

use Data::Dumper;

sub b {
    print "123"
}

$hash = {"a",sub {print "abc"}, "b", \&b};
$Data::Dumper::Deparse = 1;
print Dumper($hash);
[download]

But there is caution stated in the doc, check it.