It is possible to brake two people up without knowing on of their names. However, it wouldn't be done in the traditional since. Rather, you'd have to use a different type of spell (A bad luck spell, or the like) on the person who's name you do know; this could lead to that person no longer being in a relationship.
That's just one example of how it could be done, there are many other ways you could get creative. However, it isn't advisable to meddle with the (love)lives of others. Instead, try casting a love spell that's meant to help bring love into your life. That's simple, that's clean, and that's a good way to find happiness without hurting someone.
If you'd like to know more about either part of my post, please feel free to message me.