I think you have some serious misconceptions. While your HUSBAND isn't required to oblige himself to Virginia residency requirements, that DOES NOT apply to you and the kid.
An SS-5 also does not change your name, PERIOD. All it does is let the social security administration know of your otherwise legally changed name. Since you were recently married, you can probably assert his surname via that (you need to tell me WHERE the marriage took place). You can not just automatically change the child's name.
You will need to go to JDR court to get a minor's name changed in Virginia. First, you must have resided here for six months before it will even be considered. Second, if you know who the father is (regardless of whether or not he is listed on the birth certificate), Virginia requires him to be notified. You need to prepare the petition and order of name change which need to be signed in front of a notary. The (biological) father will need to sign the petition as well or you will have to file proof of notice. If you don't know where the father is (or who he is), you'll need to publish a notice in the paper.
All of this is a bit involved for a DIY (though it can be done). Often the local military installations have family legal assistance (or at least can steer you to appropriate counsel) on base.

