There is no reg for the rec that says the name has to be on Trotline Float. Only that they be the same size and color and a minimum size of 12" or 10"x12" if not round or cylindrical. The reason, IMHO, is that it is hard to disclaim any part of a trotline if the man catches you running it. (Once it's on your roller the whole line is yours. If it's illegal your caught) If you had 100 traps in the water it would be hard to catch you running all 100 from a distance. If the name did not have to be on them you could say. "Only these 30 are mine, those others are someone elses, he just left I'm sure he'll be back." DNR would then have to let the traps in the water until the end of legal hours before he could take them. If it's 8am do you think he's waiting around till sunset? Not! Since the law requires a name on them, if you don't claim them then he can legally remove them right then and there.
Basically it's an enforcement tool for the traps that you do not need with a trotline. It's easy enough to sit at a disance and see you begin running the trotline which is all he needs.