The name of the Klingon Imperial Empire is translated from Klingonese into English.
And possibly it is translated into English badly. And the meaning of words can change over time. Words can have two or more different meanings at the same time. Different words can mean the same thing. But if two words both have several meanings, possibly those two worlds are synonyms in only one meaning each and the rests of their meanings are different.
For example the word "prince" has several meanings in English. The one I was most familiar with was a title of a member of a royal family, so when I read The Lord of the Rings I was confused by Imrahil, Prince of Dol Amroth.
Other meanings of prince include a generic term for a ruler, and a ruler of a semi independent state or principality, which Imrahil is an example of. In the German language a prinz is a member of a royal family, and a furst is the ruler of a principality, but both words are translated into English as prince. Prince is derived from, and sometimes used to translate, the Latin world princeps.
Considering how quarrelsome Klingons are, it must be rather common for group os of KLingons to revolt and form their own independent states, which may last for sorter or longer times before being reunited with the main Klingon state or conquered by their enemies. Thus at any one time there may be more than one Klingon state in existence.
So if there are a bunch of independent Klingon states at the same time, they might all use "Klingon" as part of their names to show that each is ruled by Klingons, though the majority of the populations of some or all of them may be non Klingons suffering under Klingon Rule.
So, for example, "imperial" might mean "with an emperor as monarch" or "having the right to rule all the universe", and "empire" might mean "state with an emperor" or "the rightful government of all the universe".
So if those meanings are combined into Klingon Imperial (having the right to rule all the universe) Empire (with an emperor), or into Klingon Imperial (having the right to rule all the universe) Empire (state with an emperor), the use of imperial to modify empire might not be redundant.
Other Klingon states might be named the Klingon Royal (with a king as monarch) Empire (the rightful government of all the universe) or the Klingon Imperial (having the right to rule all the universe) Republic (having a republican form of government), for example. There could have been dozens of Klingon states with two, three, or four word official titles.
But I think that there should have enough enough separate Klingon states at the time of "Sins of the Father" that Picard has to use the full title of "Klingon Imperial Empire" to make certain that the Enterprise went to the capital of the right Klingon state.
The Wikipedia article Boer Republics lists 19 Boer Republics existing during the 19th century, with as many as five existing at the same time, an example of an ethnic group having more than one state at the same time.
Do you know how many different Roman Empires there were? I haven't counted them all.
For a few years in the 1220s, an era where some people might think there weren't any Roman Empires anymore, there was a state in western and central Europe that used the names of Roman Empire and Holy Empire and was starting to combine them into Holy Roman Empire. In eastern Europe and western Asia, there were four states, each named the Roman Empire, called Romania ("Roman Land") for short. Modern historians tell them apart by inaccurately calling them the "Empire of Thessalonika", The "Latin Empire of Constantinople", the "Empire of Nicaea", and the "Empire of Trebizond" or "Trapezuntine Empire". Warning to time travelers - Don't use those names in the past if you want to live!
In addition, the ruler of the Second Bulgarian Empire may have begun to use the title of "Emperor of the Bulgarians and the Romans". And a large part of Asia Minor was ruled by the "Sultan of Rum (Rome)".
During the 16 to 18 years from 1355 to 1371/73 there was the Holy Roman Empire, the remains of the so called "Latin Empire", with the emperor usually in exile in western Europe, the "Empire of Trebizond", and the restored eastern Roman or so called "Byzantine" Empire. Plus the "Empire of the Serbians and the Romans" and the other "Empire of the Serbians and the Romans", "the Empire of the Bulgarians and the Romans", and the other "Empire of the Bulgarians and the Romans".
And what was the title of the Roman Emperors? Don't assume that since emperor is derived from imperator the title of the Roman Emperors was imperator. from about 27 BC to AD 284 the title of Princeps was often used by the emperors, so that period is often called the Principate. About 284 Princeps was abandoned, and the title of Dominus was often used by the emperors, and that era is often called the Dominate. So Princeps can mean emperor as well as prince.
Other titles of emperors were imperator, Caesar, and Augustus. There were eras when the heir to the throne, or a junior emperor, used the tittle of imperator Caesar, and the emperor, or the senior emperor, used the title Imperator Caesar Augustus. So an imperator Caesar, and even more so a plain imperator or plain Caesar, was lower than a full imperator Caesar Augustus.
In the time of the Komnenos Dynasty (1081-1185) the title of Caesar had been reduced to fourth in rank, below Sebastokrator and Despot.
In the eastern, Greek speaking, part of the Roman Empire, the Latin imperial titles were often replaced by Greek titles. the emperor was often called Basileus, which original meant king, but was used more or less in the sense of "The Only King, Ruling the Whole World", when used to describe the emperor. By about AD 900 the title of the senior emperor, the one who actually ruled, was usually Basileus kai Autokrator ton Rhomaion, which is usually translated as "Emperor and Autocrat of the Romans".
However, Autokrator had usually been used to translate the Latin imperator so it can be considered to mean emperor as much as imperator does. Thus the title Basileus kai Autokrator ton Rhomaion can be translated as "king and Autocrat of the Romans", "King and Emperor of the Romans", or "Emperor and Emperor of the Romans".
The early Holy Roman Emperors used the title of Imperator Augustus, which may mean "emperor" or "emperor emperor". By about 1200 the person elected emperor used the title Rex Romanorum et semper Augustus, "King of the Romans and always Emperor" until crowned in Rome, and then the title of Imperator Romanorum et semper Augustus, "Emperor of the Romans and always Emperor".
Medieval rulers of Georgia used the title of mepet mepe, Georgian for King of Kings, and some also used the title of shahanshah, Iranian for King of Kings.
So there are some real life examples for the "Department of Redundancy Department".
