Another possibility that has not been discussed so far is that Ennis very deliberately signs the postcard "Ennis del Mar" as he knows that it is quite likely that Lureen will read it before Jack. After all, he may well recall that it was Alma who first let him know that he had a postcard from somebody called "Jack".
We have only one address for Jack and Lureen:
RFD 2
Childress, Texas
I don't live in the States - I live in Canada - so I'm not sure what "RFD" stands for but I assume it's a post box of some sort. If I'm right, then presumably Lureen was as likely as Jack to pick up the mail and, when doing so, would surely have looked at the postcard and the name of its signatory, "Ennis del Mar". However, that is an early address. But even if they had moved on since then, it is still quite likely that Lureen would have seen and read the card before Jack.
None of us can know what was going through Ennis's mind when he asked Jack to meet him at Pine Creek on November 7., though this may be the first time that Ennis has been the initiator of one of their reunions. If that's true, I think it is important. As important, is that this will be their first meeting after their last highly emotional and explosive meeting earlier on in the year.
Although we can't know what was going through Ennis's mind when he dent the postcard, some of us have wondered whether Ennis, is now starting to think not so much about a continuation of their old life but a new beginning. Even if he is not yet ready to fully commit, maybe he is starting to consider the possibilities of that "sweet life" offered him by Jack all those years ago.
If that's going through Ennis's mind, then signing the card "Ennis del Mar" is not so much directed at Jack as at Lureen. I don't know if it is a challenge, but at least it's insisting she knows fully the name of this man who is inviting her husband to join him - an invitation, obviously, which does not include her.
Even if this is not he case, Ennis is making sure that Lureen knows exactly who he is. He is not just some guy called "Ennis" but a fully realized individual. There is only one of me, he seems to be telling Lureen, and my name is Ennis del Mar.