What do you call it when a name/word is better known by a pejorative?

A while back, the US Congress passed a bill called the “Patient Protection and Affordable Care Act”. The bill quickly became known as “Obamacare”. During the time prior to when cannabis was made illegal in the United States, proponents of its prohibition called it “marijuana”.

In both cases, a thing with a proper name became known by a pejorative to the extent that many people wouldn't even recognize the proper term for the thing.

Is there a word or expression in the English language for describing the situation where a thing becomes best known by a pejorative term?

I'm not sure OP's two specific examples are particularly good ones, but it seems to me what we're talking about is:

Dysphemism the usage of an intentionally harsh (rather than polite) word or expression; roughly the opposite of euphemism.

Better examples (taken from the Wikipedia article in the first link above) of word triplets illustrating Dysphemism / Orthophemism (neutral) / Euphemism are:

• terrorist / rebel / freedom fighter

• dorky / quirky / original

• fat / obese / chunky

But of course any originally "neutral" term can acquire negative connotations in either the population at large, or some subset thereof, simply because of the attitudes of speakers to the referent itself. For example, many people today perceive some words like banker, capitalist, management, wealthy, politician etc. as inherently "pejorative". If they needed to reference such concepts in a context where they didn't want the negative overtones, they'd find some "euphemistic" circumlocution ("My husband works in financial services").

I think that in answer to previous questions like this, suggestions have included parody and caricature (somewhat non-specific to mocking names) as well as dysphemism. But also consider calumniation, aspersion, malignity, defamation, travesty, mockery, lampoon, japery. Terms infamity and defamity might be suitable, if they were words. Nomen dubium (Latin for "doubtful name") is a technical term meaning a scientific name that is of unknown or doubtful application.

I don't know of a word or phrase which exactly describes the situation you propose. There are a variety of reasons why certain names for anything become more popular than other names, and sometimes a term does not become perceived as pejorative until some time after it is coined. While Obamacare is currently a favorite term of its opponents, The Atlantic blog notes that its origins are not so starkly negative: it may owe its popularity to newspaper headline writers trying to save space. Given the initial popularity both of the president and the bill, it might have become a positive sobriquet.

We could make a case then that what happened here is appropriation, the adoption of a word and shifting its meaning or perception. Obamacare may have started relatively neutral, but became a term of diminution because it was the name preferred by its opponents, like Reaganomics or Thatcherism. A related term we tend to hear more about is re-appropriation, where members of a stigmatized group adopt a label as a matter of pride and identity. Textbook examples are sans-culottes, queer, and redneck— the blog post suggests Congressional Democrats have no interest in reclaiming Obamacare, however.

Another sociological term is labeling, whereby some non-conforming group is assigned a label and excluded. Although not applicable to this example, it is a related concept.