The best-known dinosaur name in all of paleontology is Tyrannosaurus rex, the "Tyrant Lizard King". Everyone the world over knows those 6 syllables. The original publication, from 1905, was written by Henry Fairfield Osborn can be read here.
Names are important. They allow us to speak about dinosaurs in a general sense. Instead of saying, "CM11338 looks different from USNM 10865" one can say, "Camarasaurus looks different from Diplodocus". The use of these genus-level names automatically includes all other specimen numbers that have been assigned to those dinosaurs. We can certainly discuss the merits of certain specimen numbers belonging to certain a certain genus but, overall, a genus is defined by a specific suite of characteristics that no other genus possesses.
Genera with similar enough suites of characters are grouped into a Family level, which allows a way to talk about groups of animals much easier. A Family level of organization allows us from having to talk about all of the individual genera, "tiger, lion, leopard, and cats" to simply saying "Felidae" when we want to talk about cats at a higher level. The same can be done when we want to talk about "wolves, jackals, foxes, dogs, coyotes" we can simply say Canidae. Using a Family-level relationship term makes it easier to discuss evolutionary trends across groups of animals, for instance. When I say felid or canid a vision of cats and dogs comes to mind to all members of our discussion.
There is a group of scientists that study names, and there is an organization that maintains naming rules, the International Commission on Zoological Nomenclature, ICZN for short. After all, lots of people may think a name is cool and use it for different kinds of animals. Why should a Komodo dragon not be called a Tyrannosaurus? After all it truly is the "Tyrant Lizard" of its range! Naming animals the same genus would cause all kinds of difficulty in using names, if Komodo dragons had been also called Tyrannosaurus, how would you know which animal a person is talking about? And it certainly would preclude the use of Tyrannosauridae in talking about Tyrannosaurus and its relatives, it would just be confusing!
Tyrannosaurus lends its name to a Family of carnivorous dinosaurs, the Tyrannosauridae, that were the apex predators in their respective days. From the "classic" meat-eaters like Albertosaurus, Daspletosaurus, Gorgosaurus, and Tarbosaurus to those you may not have heard of, Alioramus, Bistahieversor, Dynamoterror, Nanuqsaurus, Lythronax, Teratophoneus, and Zhuchengtyrannus, all of these animals were typically the heaviest, strongest, and most fearsome animals wherever they lived and they all shared characters that suggest they are all related to one another in the way canids are dogs and felids are cats. Since the 1970s, when dinosaur studies exploded, the Tyrannosauridae has been the de facto term used for the most awesome of theropod dinosaurs (ok, I'm biased here, I like Tyrannosaurus!). To scientists and dino-fans, Tyrannosauridae means something specific. But what about Deinodontidae? What dinosaurs come to mind when you see that term? Nothing, right? As it turns out, one can make an argument, using the ICZN rules, that Tyrannosauridae isn't the appropriate term we should use, but, instead, all tyrannosaurs as we know them today should be called members of the Deinodontidae! What??? Yep. Rules are rules.
To understand why this travesty of name changing could conceivably happen I encourage you to read a paper that came out in April of 2020 by Changyu Yun, with the wonderfully academic title of, "Case 3185 - Tyrannosauridae Osborn 1906 (Dinosauria Theropoda): proposed conservation by reversal of precedence with Deinodontidae Cope, 1866 and Dryptosauridae Marsh, 1890". Be warned, you will need a scorecard to follow the craziness of the early days of paleontology, the forefathers of paleo named new animals off of scrappy, sometimes non-diagnostic, material. Their early work (in their defense it was early, no one really knew what was going on, they did the best they could I like to believe!) has led to some interesting challenges in the 21st century of paleontology naming. Yun does a fantastic job of justifying why Tyrannosauridae should stay the name and not be changed to Deinodontidae.
Lest you think this is all pedantic, that there is no way the ICZN would go with Deinodontidae, remember they are a governing body and they follow the rules. The rules clearly state the first name takes precedence. Eohippus, the "Dawn Horse", (such a lovely name for one of the earliest horses), was changed to Hyracotherium because it was discovered that the material named Eohippus was the same as that of Hyracotherium and, since the latter was named first, Eohippus had to go. Even though the name means "hyrax beast" has nothing to with horses. Anatosaurus became Edmontosaurus. Brontosaurus became Apatosaurus (no, I don't think Brontosaurus should have been "resurrected"). Could the much-beloved, worldwide-embraced, term Tyrannosauridae actually be replaced? Technically, yes. That person would be universally derided as a villain (ok, maybe not THAT harsh) and forever linked with ruining a perfectly grand Family name, the Tyrant Lizard Kings (great band name!). Thankfully the amazing data assembled by Yun makes it not only difficult but, if he wins his case, it would be impossible. The wheels of nomenclatorial justice grind slowly...
Addendum - recently Tyrannosaurus rex was split into 3 species. It was published in a peer-reviewed journal and met all of the initial rules for being a legal name change. Whether it stands remains to be seen!