Hello! Project loves this trope. Some units include: Morning Musume Tanjou 10nen Kinentai, Athena & Robbikerottsu, Country Musume ni Ishikawa Rika (and later ni Konno to Fujimoto), Taiyou to Ciscomoon....
John Jacob Jingleheimer Schmidt, from the song of the same name.
Song Laura Jenna Ellinoora Alexandra Camilla Jurvanen by Finnish band Leevi and the Leavings
In Povel Ramel's song Karl Nilsson (which is a parody of 19th-century broadside ballads), the eponymous character's mother was named Sara Beata Johanna Elvira Johanna Katrina Karolin Gustafva Pernilla Johanna Therese Albertina Johanna. His father's name was Kurt.
From the Paul and Storm song Nun Fight: "Sister Maria Teresa Garcia Graziela Aguilera Delgado Francisco Diego Arroyo Inigo Montoya Zapata Paquito El Guapo Abuelita de la "Boom Boom" Mendoza"
Danny Kaye in the song 'Lobby Number' had a character named: Heinrich van Schlupen van Holdens-velerdener Hayden De-Blubeder Ulks-Geshmerzen Behausen Geuldiger Hulmeder-Helmeder Flormendeger De-Plauden De-Ults-um-Heumendeger Haskleimeder Elden-Gormen Urtsengorden Eltsenheinden gehol el-mneeyeerbehyber-ha-ha-haur (The Dangerous German Spy)
In Tales From The Afternow, everyone's name has their company, job title, IP address range, given and family names, and number of life extensions (i.e., how many times their life has been extended by artificial means, including - but not limited to - cloning, cybernetic augmentation, and genetic manipulation). The end result is names like "Independent Librarian Dynamic Sean Kennedy the Sixth".
Tim Wilson's 'Nascar Song'
She named me Dale Darrell Waltrip Richard Petty Rusty Awesome Bill Irvin Gordon Earnhardt Smith... Johnson, Jr.
A camp song: "Hagdalena Magdalena Hootensteimer Watenheimer Hogan Logan Mogan was her name!"
There was a Norwegian punk band called "Morten Jørgensen og Spekkhoggerne som fulgte etter danskebåten uten å røre spyet som rant fra ripa", which translates to "Morten Jørgensen [the lead singer] and the killer whales who followed the Denmark ferry without touching the vomit running from the railing".
The Cologne-based band L.S.E. made a song titled "Kopfe sneide" which is about the famous Spanish matador José Maria Manuel Fango Paco Carrera de Cadentes. He admits himself that his name is too long and that that's the reason why the ladies call him El Condomes instead.
Brazilian band Jorge Cabeleira e o Dia Que Seremos Todos Inúteis (Hairy Jorge and the Day We Will All Be Useless).
Due to legal reasons, the mid 80's reformation of Yes could not use the name, so instead named the group after themselves. "Anderson Bruford Wakeman Howe" was the result, and even the members of ABWH themselves admitted it sounded more like an accounting firm than a rock band.
Our Manager Told Us That Our Band Name Was Too Long and Difficult to Remember and That We Had to Change it So After a Long Brainstorming Session We Came Up With This One Because All the Other Ones Sucked. That is really all that needs to be said
65daysofstatic has a few songs and albums that get into this territory, like "I Swallowed Hard, Like I Understood", "Install a Beak in the Heart that Clucks Time in Arabic", "Drove Through Ghosts to Get Here", and The Distant and Mechanized Glow of European Dance Parties. Yeah, we don't know what they mean either.