Generican Empire

This is the tendency for space states not to have an actual identification beyond a generic term for a given political system. Often this is specified a little by equally generic terms such as "of planets". But there is no identity with any local culture. Writers can justify this by explaining that past conquerors decided that it was bad politics to hurt their subjects' feelings more than necessary. This is partly a result of Good Republic, Evil Empire: Republics or The Kingdom are generic goodness, empires are simply evil, and that's all that needs to be said.

Examples of Generican Empire include:

Anime and Manga

Code Geass has The United Federation of Nations, either justified or made worse that their only shared ideology is their utter hate and wish to defend from The Empire.
People Liberation Acting Nation of Technology from Mobile Suit Gundam SEED.

Film

Star Wars: The Galactic Republic, which Palpatine turned into the Galactic Empire. (The trend continues in the Expanded Universe with the New Republic, then the Galactic Federation of Free Alliances...) Also, the separatists are officially the Confederacy of Independent Systems.

Literature

David Weber's Dahak series (Mutineers' Moon, The Armageddon Inheritance, Heirs of Empire) has the Fifth Imperium. And the Fourth Empire, and the Fourth Imperium, and the Third Imperium and... well, you get the picture.
Played straight in The History of the Galaxy series with the Confederacy of Suns (which doesn't actually include the Sun) and the Stellar Khalifate. Averted with the Earth Alliance.
The Galactic Federation in the Sector General books, which strictly speaking isn't confined to a single galaxy.
Present among the more important entities in Isaac Asimov's Foundation series, including the titular Foundation, the Galactic Empire, and the Union of Worlds (founded by the Mule). Technically, the term "Foundation" is a remnant of the Encyclopedia Foundation, whose original perceived purpose is abandoned after the first few decades. And, of course, the Second Foundation. Averted with many of the smaller states that arise during and after the Empire's collapse, which are generally named after the old Imperial provinces and/or the capital worlds of the new states.
Dune has the Imperium, officially known as the Galactic Padishah Empire. The prequels have the Synchronized Worlds and the League of Nobles, as well as another unnamed Empire preceding both.

Live Action TV

Star Trek: The United Federation of Planets.
- By contrast, Klingons still consider themselves Klingons, and Romulans still regard themselves as Romulans. No crisis of ethnic identity there.
  - Of course, both the Klingon Empire and the Romulan Star Empire include other species as well. The just aren't given equal status and are really only mentioned in the Star Trek Expanded Universe (there is a novel where both the Federation and the Romulans are offering membership to a civilization that has recently discovered warp drive; while the choice would seem to be a no-brainer, the race ends up going with the Romulans, as they need stability more than they need freedom).
- Played straight with the Dominion.
- Also averted with the Mirror Universe Evil Counterpart the Terran Empire but played straight with the Alliance.
  - Not necessarily. While it is often just called "the Alliance," the full name is the Klingon-Cardassian Alliance.
The Alliance in Firefly, though technically, the full title of the government is "the Union of Allied Planets." There's also the "Hands of Blue" and the "Academy," though both of those are actually nicknames for specific people or organizations, and the Operative, which is, well, a title for a secret government agent.
The Systems Commonwealth in Gene Roddenberry's Andromeda. The name doesn't sound like something that stretches throughout three galaxies. Averted with the Nietzschean Empire that never arose.
- Also averted with the Vedran Empire, which preceded the Commonwealth.

Tabletop Games

Traveller: The Third Imperium
- The Third Imperium even went this one better by changing it's capital's name from Sylea to "Capital"
  - Arguably justified. While the Third Imperium began as what was effectively a Sylean Empire, it became an empire glued together by it's upper caste rather then by a core ethnicity. It probably would have been diplomatic to not stress the Sylean origins.
- Other states are less bland about it. The Terran Confederation was the TERRAN Confederation long after most of its population grew up on other planets and were of mixed Solomani-Vilani descent.
- And the Vilani before them were blatant about their Vilani origins. But one of their empire's names is the Ziru Sirka which means Grand Imperium of the Stars.

Video Games

The games in the Space Empires series even have a list of generic empire names and titles, all of which are cosmetic. Starting in SE4 however, you can define the political system your civilization adopts. Which doesn't prevent you from calling your very loose federation an empire.
- It never stopped the Holy Roman Empire, later the Holy Roman Empire of the German Peoples, from calling itself one.
Humanity's spacefaring government in Mass Effect is the Systems Alliance.
The United Nations Space Command and the Covenant in Halo.
The Wing Commander series features the Confederation and the Border Worlds.
The Avernum series lampshades it with the Empire, which is described as "Not the Something Empire or the Empire of Something. Why bother with names, when you are the only Empire around?"

Western Animation

Teenage Mutant Ninja Turtles: The Federation - in opposition to The Triceraton Republic
- In the 80's cartoon, they were called the Triceraton Empire.

Real Life

The Hanseatic League which dominated the Medieval Baltic (the word Hanse roughly means "merchant's guild", at least for older examples).
The League of Nations and the United Nations, although those don't claim to be states.
The actual name of what used to to be the British Commonwealth (and before that the British Empire) is the Commonwealth of Nations.
The Union of Soviet Socialist Republics was a description of the supposed form of government, with no reference to geography or nationality (a "soviet" was a kind of local workers' council). Of course it just lead to the rest of the world referring to the people (or at least the leaders) thereof as "Soviets".
The Commonwealth of Independent States, the organization that replaced the USSR.
Silly but real: the Miss Universe pageant is hubristically generic in name, considering that no one from outside of one local planet has ever been allowed to compete. At least, as far as we know.
The United States of America is often referred to as simply "the United States", especially in formal contexts such as official titles like President of the United States or Supreme Court of the United States.
- Something similar happens with the United Kingdom of Great Britain and Northern Ireland, though using "the United Kingdom" is not really seen outside of formal contexts.
Assorted sporting events that banner themselves as "World Series" - especially since they universally neglect to specify which world and almost never have representation from the whole world. Baseball is among the worst offenders of the latter type.