Suppose you have a man named Simcha. May he marry a woman named Simcha? (sources)
In "What's in a Name", the English translation of Zusha Wilhelm's sefer "Ziv HaShemot", the following is stated:
Some are particular not to marry a woman whose name is the same as one’s own. (See Maasei Ish, Choshen Mishpat 7; See also Sdei Chemed, entry on Chasan VeKallah paragraph 7; See also Otzar HaPoskim, Even HaEzer end of ch. 2, and the Testament of R. Yehudah HaChassid 21)
I got a hold of the printed book and added the sources to this answer. The book itself not only brings the sources, but quotes most of them.
I saw in the name of Rabbi Chaim Kanievsky that one of them should add a different name.
According to Gitin 34b, if someone is known by two names and wants to divorce his wife, we write, "so-and-so and any name he has," and the same for someone who wants to divorce his wife who is known by two names. Elsewhere (though exactly where escapes me) it also says that when there are two people in the same city with the same name we add on "son of so-and-so" and go back as far as we have to and/or give as many other characteristics as we have to, in order to properly identify the person in question.
It would seem to me that we would do the same here - expand on their names and/or list characteristics to distinguish them from each other. Although, in this case, merely adding, "son of so-and-so" and "daughter of so-and-so" should suffice for identifying the man from the woman.
Yes. I know two Elis who married each other.