Totally sucks man. Eh, just cross it out and write underneath it your proper name.

Joking of coarse.

Actually for me, not. "You don't need to see my identification." waving them off. I'd refuse to wear my ID card if I told I had to (yeah, not very good role model am I? shame on me for trying to lead you to the dark side with my rebellious ways).
Actually this applies everywhere for me, similarly being with all jobs I've held that required a nametag (friggin' retail), like first couple months at my job I wore my nametag, but once I felt I could get away without wearing it I stopped putting it on, its been sitting in my locker for what 9-10 months. I'm really surprised my boss never said anything about it. Not an issue with my name as with you since mine was changed long ago. But I have several gripes, first its no ones business what my name is unless they ask, then I have no problem with that, but can't stand when someone who doesn't know me comes up and refers to me by name as if they know me on some personal level. The other, the damn thing gets in my way while working. I look like I work there because I'm always working something out, and if they question me the usual question, "do you work here?" Yes, I do. Wha'dya need? They tell me, I help them, simple as that. No name tag needed.
But in your case, perhaps its a security issue, make sure only those that are supposed to be there are. Can't you talk to someone in charge about it?