A few of the the Christians out there who are advocating that Christians stop getting Marriage licencees, like I believe. Still advise Christians to document the marriage with a certificate signed by the couple and two witnesses, in case legal proof of the marriage is needed later.
They say the State should not give permission to marry, but does have authority over marriage in cases of divorce and adultery. And then decry that the state today allows divorce for any reason and doesn't punish adultery as a crime. And one calls for the state to make "sodomy" illegal to solve the Gay Marriage "problem".
I just talked about why there was civil authority over marriage in the Old Testament and why that's invalid under the New Testament.
These people are only talking about how the modern concept of legal marriage developed only since the 1800s, how the marriage license was originally only for giving permission for "interracial" marriages which were originally illegal. But not willing to address that maybe Traditional Christianity went wrong waaaay before that.
Even the "Pastor" or whatever you want to call that office is not an appropriate third party to bring in. No spiritual leader presides over the marriages in Genesis 2 or Revelation 19. Even when under the Law of Moses, you never heard of a Priest or Levite or Prophet having marrying two people together as one of their responsibilities. And it's certainly not covered in the Pastoral Epistles or any of Paul's teachings on marriage.
Don't put your Marriage on paper at all, paper is as worthless as the federal reserve notes printed on it.
The only Biblical Requirement for Marriage is for the Man and the Woman to agree to be married, to make a commitment to one another.
As for divorce,
First, Christians should not get divorced, the one excuse Jesus theoretically allows when debating with the Pharisees under the Law of Moses (prostitution), is still for Christians invalidated by our command to forgive.
Second, if the state wasn't involved in starting the marriage, why are they needed to end it?
As for Adultery, the punishment for Adultery under the Old Covenant was death, which is done away with under The New Covenant in John 8.
Matthew 18 and 1 Corinthians 6 and some other places talk about how Christians should resolve disputes among ourselves, within The Church. No third party, the state included, should be brought into it. Based on this many evangelicals agree it's a Sin for Christians to ever sue each other. I don't know why people have trouble realizing that that should include marriage disputes.
BTW, I don't even think Christian women should change their names. The Family Name concept wasn't really in Biblical Culture, you were just refereed to as a relative of someone or from a certain town, or by profession, to distinguish you from others with the same name. And besides that the woman's identifier being the one to change reflects the women as property aspect we should reject under the New Covenant.
If you feel called by The Holy Spirit to change your name or give yourself an additional name to reflect being a new creature in Christ, which there is much Biblical precedent for, that can be done legally for males and females. But marriage isn't a reason to do that.