I am concerned about a marriage oath before God. My girlfriend's birth certificate and social security card have two different last names due to her mothers error 20 years ago. Everyone in the system gives her the run around and we cannot get this fixed. Because of this, she cannot obtain an i.d.; therefore, we can't get a marriage license. So since we can't make it legal, would an oath before God be enough?
If the government interferes with doing what is righteous, then you do things God's way. However, I believe in your case you can get this straightened out with the help of a lawyer. It might cost a bit because you'll have to pay for the lawyer's time, but he'll know where the proper paperwork will need to be filed. She will probably have to go before a judge and get a formal change of name. It is a hassle, but it will be worth it in the long run because she will constantly run into problems if this matter is not fixed.
If you can't wait to get married talk to a preacher about what you need to do to get properly married and then square things with the government when you can. But I would strongly suggest that you get the problem straightened out first because the process might reveal other problems which you'll need to address before you get married.