Legal Marriage
Typically, the officiant can sign your marriage license on the same day as your public ceremomy and make your commitment legally binding then and there. However, there are situations when this is not the case, so it is best to think this through first.
First the officiant needs to be licensed in the state/ region where the marriage is taking place. If he/she is not, then you can still complete a religious or symbolic ceremony, however the legal element would need to managed separately (before or after the public ceremony). In such cases, it is considered best to do the legal marriage before your religious ceremony, so that when you are announced as a married couple to your family and friends, this is the full truth, no caveats.
It is also important to check each state and county rules. Different states have different rules regarding marriage laws. Some states require blood tests, others have timing restrictions, perhaps the ceremony must take place within 30 days of getting the license, or perhaps they have a required waiting period of 1 day.
Learn more about legal marraige and name changes here.