Can we make changes in name in the marriage certificate

We got marriage certificate issued in 2014. The name of my wife was given as "A B C". Her original name on birth certificate (and all other govt issued documents) is "A D C". Her middle name was changed before marraige in 2012. (She was adopted, so her middle name was changed). We had made affidavits, newspaper ads, etc for the same. When she went for issuing "Passport", her marriage certificate was rejected. Reasons: the adoption is not possible for any child after age of 18 years. So basically her name change is invalid. Since marriage certificate was the only document, that she had with new name. We decided to change the name on marriage certificate itself. Is it possible?