Am I legally married if my ex spouse uses the wrong name on our marriage license

First where is this at, China? Mexico? Iraq? If the US, which state?

If in America how did they do that, since official ID is required when getting a marriage license.

Also you say "ex spouse" so are you already divorced? If divorced, then you are not married, no matter what name they used on marriage license. The divorce will name he specific marriage that you had.

If there is no divorce, merely using an incorrect name, does not make the marriage invalid, but it may, but you would have to go to court to have this done.