Hyphenated Last Names and Infinite Sets

I like thinking about ways to get to infinity. Not that this is possible or anything. One that came to mind was after hearing about some friends of mine having a baby. They have hyphenated last names. If the names are passed on to the kid and then that kid grows up and meets Miss Right, and Miss Right also turns out to have a hyphenated last name, they could have four names in their last name. And then! If their kids meet other kids who have quad-names, they could double to ocho-names! And so on till infinity.

Well not quite, but you get the idea. But maybe this could be an argument against (everyone) taking a hyphenated last name.

(Or not).