Interesting question, Chow. The story doesn't give any clue about how Ennis signed his name, so I guess we must attribute this plot detail to the prop director, set designer, or Ang Lee himself. But it may be that Annie had a hand in it because of her earlier novel called Postcards in which each chapter begins with a picture of a postcard written by one of the characters, usually Loyal. I'll have to check the book and see if he signed his full name, Loyal Blood.
After he omitted his last name in introducing himself to Jack, Ennis used his full name twice, first to Cassie and then to Jack in the final postcard. It's clear that Cassie was just a Jack substitute so it's not surprising that Ennis said his full name, almost in an experimental way. In signing his full name to the postcard, Ennis seems to be acknowledging that through the experience with Cassie he learned how to give one hunerd percent of himself, not just once in a while way out in the middle of nowhere, but consistently. I don't think he was being formal or distancing himself at all, I think he was doing the opposite.