It's much easier to tell people apart with search engines and even library cataloguing systems. These names tend not to come during the lifetime of the person, but usually long after, and often from different places. "They had that king Karl, which Karl? The one that was a tyrant." "Ah, right" "Alexander did" "Which Alexander?" "Phillip's son" "that really doesn't narrow it down." "The great one" "oh, right"

The other side are names that come up because of propaganda, especially attempts to bolster an image or to diminish a reputation after the person has died. These are more popular within that country, and usually more close to said person's lifetime. Think "Dubya" in America for GWB. The name is unlikely to be understood by most 100 years from now, and even most children today might not understand the reference, but people of a certain age will mostly pick up what you mean relatively easily. But again, there's usually a short shelf life for these things because it's a biased term, and it's not going to show up in reference guides, encyclopedias, or official histories (at least not as one of the main important things to know about this person so it will eventually boil down to a neat bit of pub trivia or something the professional scholars of that invidual know, but won't be common outside of that small circle.

That comes in part with a rise in standards of professional academia and publishing. It was not uncommon to publish direct attacks against politicians, leaders, etc. with names of all sorts. King George "The Royal Brute" or other such "wicked tyrants". These types of publishings would be distributed as pamphlets and the like, and they could even gain popularity outside of the country it was intended for. So names might stick that way, but again, only so long as the people around to have read and remembered -- and cared passionately enough about the subject.

It would kinda be like if we named our current politicians off of names people on Facebook gave them -- but we don't, and for good reason.

Instead, these days, if you want to learn about events happening under one politician you're likely going to encounter peer-reviewed or tightly policed systems online in the forms of Wikipedia, news articles, published books, etc. More people are going to become instantly familiar with the individuals by their birth names, and instantly familiar with their role in whatever conflict. These may still need to nicknames being created (and if you search in the right places there are plenty for modern politicians), but they won't be enough to drown out all the other more polished publishings.