Hmm... I wasn't aware of this tradition either.
For our STDs I used cute palm tree ones I had that just had my name. I felt weird though... like I was leaving him out in some way.
For our invites that I'm working on now, I included both of our names because I felt weird leaving him off the first time. Never really asked Sean his opinon though... I'll have to see what he says. If you have the time/budget... I would say get new ones with both of your names if it is important to him.