Weddingbee boards

A good rule of thumb is to use the address where you want your gifts to go; people often send gifts to the RSVP address / return address (you probably want to keep these consistent to avoid confusion among your guests).  So it would make the most sense to use your FH's address for this reason.  You don't want gifts and RSVPs showing up at your old place -- you'll be getting lots of those in the beginning of the summer.

Either use just his name or both (although, for a return address, just an address is sufficient -- and may even be more proper etiquette-wise).  Using just his has the benefit that Great Aunt Maude isn't scandalized by thinking you're a loose lady... he he.  Or, you could use both names to let everyone know where you will soon be living if Great Aunt Maude-types aren't an issue.