Charles the Bald, Charles the Fat, Pepin the Short, Louis the Stammerer, Charles the Simple. I'm not sure if I would be too fond of going down in history being known for my weight, male-pattern baldness or speech impediment, especially considering the typically more flattering royal subtitles of being 'The Great' or the 'The Fair'.
Am I missing something and these sobriquets had much more flattering meanings back in the day, or does it really speak to a certain contempt that chroniclers had for a lot of Carolingian rulers, and if so why?
Personal surnames and nicknames weren't restricted to kings, but were endorsed by the whole Frankish aristocracy (given for themselves, or attributed by their contemporaneous, or later, biographers).
Twisted-Beard, the Furry Prince, the Bastard, the Bad, the Cheater, the Crooked, the Towhead all exist besides, the Black, Grey Mantle, the White (nobody "of Many Colors",sadly), the Quarrelsome, the Tall, the Pious, the Young, etc. and the lot of people nicknamed from a patron saint, a place of origin or ruling, or their function (Capetians might own their dynastic name to the Cape of St Martin, Hughes being symbolically "Caped" for later chroniclers)Some of the descriptive surnames were indeed more fashionable and prestigious (the Magnificent, the Royal, the Great, the Pious comes in mind) some...less so.
Not all lords had nicknames, at least that were recorded/attributed (for the same reason why non-aristocratic surnames didn't survive while virtually certain to have existed), but out of convenience (especially when dynastic names meant you had entire stacks of 'Charles', 'Guillaume/Williams', 'Rodolph', etc. to distinguish) as much of publicity or fame, some stuck around for the better or worse (some had more than one depending who wrote their biographies or mention in chronicles).
Some of these surnames are arguably, or seemingly, straightforward : 'the Bastard' stresses their birth, the Black their complexion or hair color, etc. But some amongst them got their meaning somewhat lost (or twisted), not always obvious to recreate or contextualize.
Charles 'the Bald' seem to have an embarrassing, petty nickname unfit for a king or an emperor, but contemporary depictions doesn't evidence he was actually lacking in hair. Several explanations had been proposed, stressing that bald shouldn't be taken at face value but could be understood as "short-haired" either following Italian or priestly fashion, an unusual sight for Frankish aristocracy (especially as tonsure was used as a marker of social/political casting out by the king) but not necessarily shameful in itself by the IXth century as being associated with religious themes (especially as hostile contemporary sources do not even point that out). The king would have been displaying scholarly and ecclesiastical values (especially as those became more readily identified with the empire during his father's reign), possibly explained for example as being made abbot of Ste Corneille (an abbey planned to rival Aachen as an abbatial royal/imperial centre), in a period when people took great consideration onto hair, their colours, their appearance, their fashion, etc. (hence other aristocratic nicknames related to that). Outside royal context, we also have the surnames as "Furry Prince" (probably misrended as Plantevelue/Plantapilosa) for Bernard II of Gothia, or "Hairy" for or Guilfred of Barcelona : while seemingly embarrassing as well (and making them sort of overgrown Hobbits), it could rather be related to a local custom for local lords (many bearing equivalent surnames) of bearing a furry cap as display of power. This explanation isn't better by the virtue of explaining it otherwise than a purely physical description, but ought to be considered giving the relative recurrence of the term in the region.
The case for Charles 'the Simple' is somewhat easier to deal with : while associated since the Middle-Ages with the idea of idiocy, intellectual deficiency, and the like, this wasn't the case yet when the surname was recorded but was rather used (and still is in a, really, archaic French) standing for "honest", "direct", "without hidden thoughts", "frank" but, probably purposefully, misunderstood by later scholars.
Still, Carolingian (and early Capetians) kings seem to have rather unflattering surnames (although surnames that actually stuck out are far in between) and while other aristocrats did, these also had fashionable or prestigious ones contrary to the kings who had to content themselves with 'the peaceful' or 'the simple'.It's quite possible that Carolingian sources underscored the distinction between a quarrelsome and warring aristocracy with everything to prove and claim for, and a more serene, simple yet royal display especially as an imperial apparatus (itself largely rooted in religious and transcendent themes) was used to reinforce a fleeting royal authority.
Eventually, it's worth stressing that a significant number of Carolingian and Early Capetian surnames are later creation, sometimes distant by centuries : Peppin III wasn't nicknamed 'the Short' before the XIth century (and not consistently originally) while he seem to have been nicknamed 'the Pious' relatively early on; Louis 'Do/Did-Nothing" 's mentions obviously are posterior to his reign and Charles 'the Fat' had not been called such before the XIIth century. Historiographic tropes and, not only though, hostility factored in our perception of these kings : late Carolingians were depicted in general as feeble, insane, tyrannic, incompetent and justly dealt with in many medieval historiographies (amusingly, pretty much as Carolingian authors described Merovingians) and that coloured some of these rulers, either due to misunderstanding of a word that shifted meaning, either making-up nicknames that stuck because it fit common tropes until the XVIIIth and XIXth centuries when these nicknames (themselves fairly informal) were 'set' once and for all in European national historiographies.
(Non-exhaustive sources, mostly for some precise exemples)