George R.R. Martin's A Song of Ice and Fire is stuffed with nicknames for the myriad of characters. Jamie Lannister (Kingslayer), Robb Stark (Young Wolf), Bryden Tully (Blackfish), and many others all have nicknames that other characters, frequently people they've never met, refer to them by. Was this ever common during and before the 18th century in Europe?
The Hellenistic Greeks were very keen on the use of epithets for their monarchs. They were often incredibly grandiose but nonetheless helpful for keeping track of historical figures with the same names. Ptolemy I was known as Ptolemy Soter (the Savior), Seleucus I was Seleucus Nicator (the Victor), Seleucus' grandson was Antiochus Theos (the God) etc. These were the more self aggrandizing examples of Hellenistic sobriquets (Soter was a particularly popular nickname) but they were often taken in recognition of something. Ptolemy I took the name Soter because the island of Rhodes bestowed it on him for saving them from a siege in 305/304 BC. Antiochus Theos got his nickname from the people of Miletus for delivering them from a tyrant.
One can also find nicknames based on physical characteristics such as Antigonus Monopthalmus (One-eyed), his grandson Antigonus Gonatas (knock-kneed), Seleucus Pogon (the Bearded, although this may have been unofficial), or Ptolemy Physcon (Pot-belly, although this too was unofficial). We also see sobriquets taken on account of personal deeds and characteristics such as Demetrius Poliorcetes (the Besieger), Ptolemy Ceraunus (the Thunderbolt), or Antiochus Hierax (the Hawk).
The prevalence of these nicknames suggests that it was common practice for a Hellenistic king to take one, making it a recurring theme in the Greek world from the late 4th century until the Greco-Macedonian monarchies died out.
They were pretty common across all of Europe. The French did it a lot and more consistently than the English. Philip the Fair, Philip the Tall, Louis le Hutin, Louis the Fat, Charles the Mad; I would say up through about 1400, more French kings had them than not. Spanish kings too had a number, some Russian as well. Personal opinion: the tradition was dying by the Renaissance for many European countries. (I've done a lot of royal/noble genealogy study)
Oh, and let's not forget the Byzantines. The Bulgar-Slayer (Basil II) was a genuine epithet, as well as Copronymus (Constantine V, who supposedly defecated while being baptised).