Well Idk if you have options but, since Odysseus was disguised, no one knew his true identity. So when he would do a couple of things that only Odysseus could do, like shooting the arrow through the axes, people would get confused on how could someone that is not him do it. Also with his scar, i think it was Eurycleia who saw it and she knows that it was a mark that only Odysseus has from his childhood. All of this brings suspense to many like Penelope and the suitors because they cant believe that someone else could have the exact characteristics that odysseus has b/c they think he's dead
hope this helps you somehow
