So we had dinner with them in Bethesda a couple nights ago. We got some hints about how to go looking for musicians, and they agonized over the same damn issues we'd struggled with on addressing. The system we came up with looks like this. Married couples using the same last name are Bob and Mary Biggedyboo, or Mary and Bob, if we know Mary better. Married couples using different last names are Bob Biggedyboo on the first line, Mary Ragnarok on the second or, again vice versa depending on circumstances.
Unmarried people get their own names and nothing else.
We felt it was simple, consistent, and avoided all kinds of potential pitfalls. The invitation just has my name. The answer is, bring anybody you care to bring. I was detailing our experience to Rick and Audrey and explained it like this. If we care enough about someone to invite them to our wedding, presumably we want them to be comfortable, to bring anyone who's important to them and with whom they want to share the experience.