If your name on your marriage certificate is Jane Doe-Smith then you are legally Jane Doe-Smith until you go to court and officially change your name to Jane Smith.

However, nothing prevents you from referring to yourself as Jane Smith and signing your name as Jane Smith anywhere except where there is some requirement that you use your full legal name.

Nevada adult name change appears to be a rather simple process and name change forms are probably available on your local court's website or from a website of a court that has them and then just change things around to fit your local court.