I believe you're attempting to order a "modern" grave marker. American soldiers from WWI through the Vietnam War were assigned "service numbers".
The Armed forces of the United States first invented service numbers on 1918-02-28 and abolished their use in 1974. The first U.S. military member to hold a service number was Arthur Crean.
The following formats were used to denote U.S. military service numbers:
* 12-345-678: United States Army and U.S. Air Force enlisted service numbers
* 123-45-67: United States Navy enlisted service numbers
* 12-345: United States Coast Guard enlisted service numbers
* 123456: United States Marine Corps enlisted service numbers
* 12345: Service number format for most U.S. military officers
Social Security Numbers are today used as the primary means to identify members of the U.S. military. The common format for a social security numbers is 123-45-6789.
You DO NOT require a service number to obtain a grave marker for a Civil War era soldier. I am going to make Mark Raines, a contributor to these sites and a man who has helped people places hundreds of Confederate markers about your posting. I'm sure he'll respond and help you with your project.
Jim Martin