Hereditary cognomina were used to distinguish different major branches of large, powerful clans. Some sort of device to specify which subbranch of an enormous group you're talking about appears to be necessary in every place that has such enormous groups; in imperial China, then as now, vast swathes of the population were covered by just a handful of surnames, but the practice developed of referring to notable families by a combination of their name and the location where they were dominant.

So Caesar's close relatives were all also called Caesar, which is how it got to be an imperial title. You might think that with the original cognomen locked into place for such families, members would get a second cognomen so that there would be at least one part of their name that could identify them. But apparently not.