The others before me have answered the exact question you asked, namely how you pass a regex, but if you want a slightly more flexible solution (and better than a string eval), you should consider passing a subreference, which you then call to modify node name. For your code above would look like:

sub change_node_names { 
  my ($self, $node, $code) = @_;
  $nodeName = $code->( $nodeName )
}

$foo->change_node_names( $node, sub { 
  my $name = shift; 
  $name =~ s/wrongnode/rightnode/;
  return $name
} );
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While this requires slightly more effort to call the subroutine, it is much more flexible as you can put literally *any* perl code inside of the annonymous sub, which is what the funnny  sub { } creates.