Calling a peak by its UTM seems ungainly especially since just one coordinate is given, and the coordinates repeat over various zones.
Perhaps, but using an elevation (e.g., Peak 13724) is even less specific. More importantly, elevation-based names are inherently unstable (particularly for unnamed peaks with no spot elevations). The entire High Sierra is in Zone 11, and there are always going to be peaks with the same name in different ranges. Therefore, I think where no unofficial name exists in common use, I favor using a name that automatically specifies the location fairly precisely.
I agree on the vagueness of names like "Peak 13724". All officially un-named peaks have this issue, and there is no consensus as to how to name them on SP. I know the Sierra Club DPS and other related clubs often give a single UTM for waypoints and sometimes, a saddle or peak. I don't have an answer myself. I've put up pages for unnamed peaks too. I usually name them after a nearby Benchmark or if it's close to another peak, call it "South such-n-such" keeping in mind its ability to be found via search engines. I also make it clear that if I named it something, it's an unofficial name. I've seen similar pages do the same and it seems to be an accepted practice.