Isn’t there a term for these types of name descriptors? Does “The Red” or “The Black” fit into that group even though they’re not as descriptive? Is it exclusively used for royalty and military leaders? Also, is there a list on the internet of historical personages with those kinds of names?
Billy the Kid
Stan the Man
Chet the Jet
Guess not. 
Interesting question, though. I’ll be looking forward to the answers.
Epithet, first definition. So sayeth one of my college profs.
The Carolingian monarchs of the Holy Roman Empire had some of the best;
Charles the Bald
Louis the Stammerer
Charles the Fat
Charles the Simple
Louis the Sluggard
Quite an impressive bunch!
Ace309. “Epithet?” Seriously? That’s it?
Wow, modern usage really pushed that term off its pedestal. They sure don’t sound like insults.
“Interesting question,” says Qadgop the Mercotan. Heh.
More amusing epithets. 
Ace309 beat me to the name: Epithet. You’ll find, however, that the vast majority of them were purely descriptive, not adulatory. Ethelred the Unready (which means Ill-Counseled, not Unprepared), Louis the Fat, Charles the Bald, Louis the Fair (light-complexioned, not evenhanded; he was a SOB at times), Erik Bloodyaxe, Ivan the Terrible (terror-inspiring), Edward the Confessor (religious bloke). Erik the Red was so called because he was of ruddy complexion and red-haired. St. Moses the Black, an Orthodox saint, was called that because he was of sub-Saharan African ancestry, and that was his epithet in life.
Oh. Well, Colibri sure cleared THAT semantic drift up, quick.
I’d like to say that Erik Bloodyaxe is a kickass name. Carry on.
Sobriquet is another word for it.
Plus, there was that one Party meeting he went to as a teenager…
“Are you now, or have you ever been, a member of a Viking Raiding Party?”
Appellation is another term for it.
And let’s not forget Castille’s Joan the Madwoman (Juana la Loca), Peter the Cruel (Pedro el Cruel), and Henry the Impotent (Enrique el Impotente)(ouch!)
And Bud the C.H.U.D.
How about Carlos el Hechizado (Carlos the Bewitched)? (Actually, that might have been Spain, not Castile.)
Kermit the Frog
They are also called cognomens or, if laudatory, agnomens or honorifics.
Or her husband Felipe el Hermoso (Philip the Handsome). IIRC, after his death, she carried the casket with his body in her carriage everywhere she went. <insert “handsome cab” joke here>.
Btw, I prefer to render her name into English simply as “Crazy Jane”.
The Polish kings had some strange names. Here are just a few:-
Boleslaus the Brave
Ladislaus the Exiled
Boleslaus the Curly
Casimir the Just
Mieszko the Old
Ladislaus the Stick-legged
Leszek the White
Mieszko the Knot-legged
Henry the Bearded
Henry the Pious
Boleslaus the Shy
Leszek the Black
Ladislaus the Short
Casimir the Great