I suppose the equivalent would simply be your fame and renown among other knights, and possibly across that Knight's corner of the medieval world, but it's important to understand that killing a Knight in personal combat wasn't really a done thing. On the battlefield, Knights were kept alive for most of the medieval era, as they were important people to be treated properly, and could be ransomed back after being captured.

As such, most of a Knight's renown would come from tournaments, whether the later tilts or the earlier melees - mock battles between sides of knights, who would usually aim to defeat and capture each-other just like in a real battle -though I'm certain plenty of knights had battlefield prowess to boast about, it's worth adding that battles weren't really a norm, but tournaments were.

So I think most people here are going to agree that William Marshal the Knight most famed for his tournament ability (though if anyone has other examples I'd definitely be interested in hearing of them) There's plenty of good information on him here: http://www.usna.edu/Users/history/abels/hh381/Chivalry.htm but for the sake of saving time, I'll quote some of it.

"William Marshal's career reflects the importance of tournaments for knights. The History of William the Marshal mentions sixteen tournaments in which William participated between 1167 and 1183. Between 1177 and 1179 [Marshal] entered into a formal partnership with Roger de Gaugie, another “bachelor” (landless knight) [...] According to a list kept by Wigain, the Young King's clerk, the two between them captured 103 knights in the course of 10 months. In one tournament William Marshal captured ten knights along with their twelve horses."