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The caller function provides access to the call stack in Perl. In a list context, it returns your package information:

( $package, $filename, $line ) = caller;

Which is not very useful. Luckily, if you give it a parameter (the stack frame number in question), it returns:

(   $package,   $filename, $line,       $subroutine, $hasargs,
    $wantarray, $evaltext, $is_require, $hints,      $bitmask
    )
    = caller($i);

So, you can use it to find out who you are, or who your parent is (I'll leave finding your grandparent as an exercise to the reader):

# Me

$me = ( caller(0) )[3];

# Parent

$parent = ( caller(1) )[3];

Rather than using caller() directly, you probably want to create functions:

sub whoami  { ( caller(1) )[3] }
sub whowasi { ( caller(2) )[3] }

A full example program:

# ignore warnings about undefs.  DON'T DO THIS IN REAL CODE
no warnings;

sub whoami  { ( caller(1) )[3] }
sub whowasi { ( caller(2) )[3] }

sub me {
    print "me: hello\n";

    # Note that whowasi() returns undef here
    printf "I Am: %s.  I was: %s\n", whoami(), whowasi();

    print "me: goodbye\n";
}

sub them {
    print "them: hello\n";

    printf "I Am: %s.  I was: %s\n", whoami(), whowasi();

    me();

    print "them: goodbye\n";
}

print "main: hello\n";

# Note that whoami() and whowasi() return undef here
printf "I Am: %s.  I was: %s\n", whoami(), whowasi();

them();

print "main: goodbye\n";

Which Produces:

$ perl ./demo.pl
main: hello
I Am: .  I was: 
them: hello
I Am: main::them.  I was: 
me: hello
I Am: main::me.  I was: main::them
me: goodbye
them: goodbye
main: goodbye