The question isn't much different from asking if a string which is a hash value can know which key of the hash it belongs to. The problem is that values can move around. What if a given value (string or sub) is the value for more than one key? The other factor that impacts how this could be done is: How are you creating the anonymous subs? If you have access to that code, then a solution might be as simple as making a lexical variable to hold the key value, which the anon sub then closes over. But again, this presumes you can programmatically prevent a value from being copied or moved to another (incorrect) key later.

sub make_sub_for_given_key
{
   my( $key ) = @_; # amongst other arguments

   return sub {
      # this sub "knows" what $key is, forever.
      print "Hi! I belong to key '$key'\n";
   }
}

my $key = "Tuesday";

my %hash;
$hash{ $key } = make_sub_for_given_key( $key );

# later on, ask each sub what key it belongs to:

for $key ( keys %hash ) {
   $hash{$key}->();
}
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