That is fine.. As far as I can remember, my husband only showed his proof of address without my name in it...it's understandable as you just arrived in the UK.
But if you really want to show a proof of address with your name in it, I'm sure you will get a letter from your surgery/GP registration in a week time.
During my time, I only started gathering my proof of address just right after the wedding...even the GP registration and things like that. I have no idea at all that fiancée visa is eligible for NHS registration, that's why I only did them all after I got married. So ignorant of me!