The tinker gnomes from the Dungeons & Dragons setting Dragonlance, as well as almost everything they name, have extremely long names (mainly because they take into account every possible detail about the thing being named, like a person's family tree or a place's history and description). For everyone else's sake, the gnomes use shorter names as well. In fact, one primary tinker gnome stronghold was named by a human, who realized he made a mistake when he asked a gnome the original name (the stronghold is now named Mt. Nevermind). In 3rd Edition D&D, gnomes in general tend to have very long names, because as a rule they love names, including nicknames, and give and receive them with equal grace.
Dragons in various D&D settings also tend to have rather long names.
Inverted with Eberron's changelings, whose real names tend to seem too short — seldom more than two letters long — to other races.
Warhammer has Tradelord Greasus Tribestealer Drakecrush Hoardmaster Goldtooth the Shockingly Obese.
In Warhammer 40,000, Tau have a strange naming system where the individual's name is, in order, their caste and rank, their sept-world of origin, and then their personal name. Some Tau gain honorific names and titles over the course of their lives, and needless to say, some particularly badass Tau can get quite a few of these. For example, Commander Farsight's full name is Shas'O Vior'la Shovah Kais Mont'yr. Fortunately, just O'Shovah works in shorthand.
Orks get nicknames (or give themselves nicknames) after some particularly spectacular feat. Thus the non-canon ending of Dawn of War gives us Warboss Gorgutz Deffscreama Bloodspilla Deffkilla Ragescreama Ghostkilla Gunsmasha Daemonkilla 'Ead'unter.
The Adeptus Custodes, personal bodyguards of The Emperor, gain additions to their name for every notable deed they accomplish. These being biologically immortal warriors armed with the greatest weapons and armor, second only to the Primarchs and their charge in combat prowess, and veterans of innumerable battles with countless foes, this happens quit often. As a result trying to say the full name of a Custodes can take hours, if not days.
As hinted by the Keychain of Creation example below, the Deathlords of Exalted have a predilection for this — it's what happens when you feed your original name to Oblivion. The nine canonical Deathlords range in titles from "Mask of Winters" and "Eye and Seven Despairs" to "The Dowager of the Irreverent Vulgate in Unrent Veils" (try saying that one five times fast).
Honorary mention goes to "She Who Lives In Her Name". Far from the longest name, but long enough to cause problems when it had to be used over and over again in a book with a very tight word count limit.
Parodied in Munchkin with the Thing With A Name So Long There's No Room For A Picture On The Card.
The Soulless in GURPS Fantasy II. Even their personal names are pretty long, but they're nothing compared to their word for themselves, which has over eight thousand syllables.
Sentinels of the Multiverse villain La Capitan has accumulated one of these during her travels across time. Her full name is Maria Helena Teresa Fafila Servanda Jimena Mansuara Paterna Domenga Gelvira Placia Sendina Belita Eufemia Columba Gontina Aldonza Mafalda Cristina Tegrida de Falcon. Word of God is she just picks ones she thinks sound nice and adds them onto her name. By the time she is La Comodora, she's just going by Maria Helena.