That's a great question. I would definitely check with your state -- they would provide you with the details you need to make a change to your company's name. In my opinion, I would take the "cross every T and dot every I" method to your business' practices, meaning I would submit a name change with my state even if it's not mandatory. If you have a potential client who wants to submit a query on your company's name, and the whole name of your company doesn't appear, your company may not appear credible. But definitely check with your state.
By the way, I really like the name you have chosen. CustomVA is actually very good on its own, as well as the addition of Administrative Services. Either way, you can't go wrong!