if name is on the deed of a home in Virginia but not on the mortgage and spouse dies do I just continue to pay the mortgage or do I have to refinance.

I would just keep making payments. If you have qualified as executor of your spouse's estate, send thelender a qualification certificate as getting information can be tricky, even though you own the property. Some lenders get hyper-technical about who they can talk with...but as long as you can keep making payments, and if the interest rate is acceptable, that's what I  would do.