I am just crossing over to clicker training. I have two dogs. Of course, formal training sessions will be with one dog at a time. So neither dog will hear the clicker or marker word without receiving a reinforcement. But should I have two different marker words, one for each dog. So when they are together and one does something I want to mark, that dog knows I am marking what it just did and the other dog does not get, either marked for doing something I do not want it to do, nor hear the marker word but receives no reinforcement.
My opinion
I do not think you need to have different words for different dogs. When you mark and reward a the dog that did the behavior correctly, the other dog will know that they didn't get a reward so they must not have done it right.
Just my tid bit
I remember in the book Reaching the Animal's Mind that Mrs. Pryor did training with multiple dolphins. But she used one whistle for the whole group. So you probably don't need it. Just my thought
=) hope this helps