Han has a Rebel rank insignia on his Hoth outfit though. 😉
So he does. I could come up with some explanation (like the only extreme cold weather gear available was what the Rebels had and provided him with, so it wasn’t official, or it’s some symbolic insignia recognizing him for his involvement in Yavin etc., or even a security level access pass for an independent captain so that he as access to his ship) but I shall stand corrected, that is a probable possible assumption. 😉