My question involves marriage law for the State of: Nevada/California

My husband and I recently got married in the state of California. We live in Nevada. We both changed our middle names (to my maiden name) and I changed my last name to his name on the marriage certificate. We went to the social security office with our marriage certificate and they accepted the name changes. However, when I went to the DMV in Nevada, they refused to change our middle names, saying that a marriage certificate is not proof of a changed middle name. We were told that we have to go through the courts to amend our birth certificates in order for our names to be changed on our licenses (a lengthy process that will cost us $200 each). If a name change is accepted by Social Security (which is part of the federal government), shouldn't it be recognized by all states? I was also told that my license has to match my Social Security card...how can I do that if the DMV doesn't accept the social security card and marriage certificate as proof of a name change?

I am SO confused and really wish that this process was not so complicated. I feel like my husband and I have a right to choose our names when we get married, and the state is denying us that right by refusing to accept our marriage certificate. I have been unable to find documentation of any laws regarding name changes and marriage in Nevada.