Maybe!
Marriage Certificates differ in terms of verbiage and formatting county by county across the US. Some Certificates will list both parties' current legal names (i.e. "Person A" is marrying "Person B"). Other Certificates will ask for one or both parties' new married names (i.e. "Person A" is marrying "Person B" and Person B's declared surname is "XYZ").
If your Certificate requires only your and your spouse's current legal names, you'll be good to go! If though you were able to list a new married name (or declared surname etc.) and you did not, you won't be able to use the Certificate for the name change. We can't speak specifically to your situation without seeing the Marriage Certificate but please note that a vast majority of Marriage Certificates will NOT list the new married name.
If you'd like, you can send an email with a photo of your Marriage Certificate to our support team: "customerservice@hitchswitch.com."