ID problems....?

You're under no obligation to change the name on the green card, but it looks like having your maiden name on it may turn into a pain in the neck. If, as another said, you showed your green card, marriage certificate, and social security in combination, most prospective employers should be able to figure it out that you're one in the same person on all three documents.

If you find an employer who can figure that out, and they hire you, your troubles are over. It's expensive to replace a green card. The choice is yours. Legally, you're fine as it is.

I would try to figure out if you could change it. My Fiance is foreign and he doesnt have his green card yet so Im not certain about all of the rules/ guidelines.. all I know is Immigration can be a huge pain in the butt and everything should be done by the book.. you should try to get in contact with the american embassy or your nearest immigration office to find out exactly what you should do... Here is a website that may help.. it was somewhat helpful to me.. but I have found that its more useful to talk to someone because the laws on immigration and what not change so often: http://www.uscis.gov/portal/site/uscis

Good Luck!

You could try showing your certified marriage certificate, but you might want to clear that up, yeah.