is there a specific term for this fallacy?

If a person forcefully injects their own definition or interpretation into a term although their definition is not accurate relative to the term/topic.

For example, if someone claims that Post-modernism includes the alienating aspect where there is always an Oppressed Group and an Oppressing Group. And the belief that everything is all about power and nothing else.

When I asked him to show any proof that this definition is at the very least credited, he sent a definition of PM that did not include what he said. Furthermore, he resorted to argument from analogy when I questioned the truth of his claim. He said: "That is like me getting the definition of a car from a trusted source where the source says that a car has an engine and body and that it moves forward and backwards. Then i add that cars also have headlights and car seats

Now I've done my fair share of research on PM and I know this is untrue, however, he still insists that this is the correct definition.

Sounds a bit like the definist fallacy , if used to make their argument easier to defend.

Definitely Definistic, but I can see a case for ad hoc rescue too.

As the others have said, it doesn’t seem to be a logical fallacy.  The correctness of the conclusion hinges of the truth (or not) of the premise about what post-modernism is.

In the P –> Q (if P, then Q) form (assuming all other premises are true), validity of the conclusion depends on the correctness of the definition.  

If it has to have lights to be a car, then a lightless vehicle can’t be a car; however, if the definition of car doesn’t mention a light, one might actually need a licence to drive that lightless vehicle.

Intentionally presenting a false premise doesn’t turn the argument or the logic into a fallacy – it’s just something that’s probably intended to influence others when logic isn’t working.  Basing an argument on a false premise isn’t bad logic; it’s just deceptive.

Found this, close to his Def? You decide. There are more at the link

https://www.britannica.com/topic/postmodernism-philosophy#ref282558:

Through the use of reason and logic, and with the more specialized tools provided by science and technology, human beings are likely to change themselves and their societies for the better. It is reasonable to expect that future societies will be more humane, more just, more enlightened, and more prosperous than they are now. Postmodernists deny this Enlightenment faith in science and technology as instruments of human progress. Indeed, many postmodernists hold that the misguided (or unguided) pursuit of scientific and technological knowledge led to the development of technologies for killing on a massive scale in World War II. Some go so far as to say that science and technology—and even reason and logic—are inherently destructive and oppressive, because they have been used by evil people, especially during the 20th century, to destroy and oppress others.