There is a friendly warning here from Groq: https://wow.groq.com/hey-elon-its-time-to-cease-de-grok/

Is it safe to say, 4 months later, that Elon is ignoring this? I assume there hasn't been any kind of response or further action taken yet.

Would be a rough trademark enforcement case as “Grok” has been in common language for decades

So has "Apple" and "Windows".

Grok and groq both relate to AI, so there's definitely grounds to believe the names may cause consumer confusion.

After all, Apple (computers) was repeatedly sued by Apple (records) for doing music things.

It's easier to get a trademark on an altered word than a plain dictionary word. Just acquiring the easier one to acquire doesn't mean you now have rights over the harder one to acquire, though eventually after enough market recognition you might be given some control over other people using the common one. I wouldn't think groq is there yet.

Robert A. Heinlein coined the term grok in 1961

Six is plural.

I myself have never heard it outside of "nerdy" circles... that is: people who would read science fiction.

I personally am not entirely happy about the word (no matter how it is spelled) being used for a particular AI product. "Grok" to me means knowing a subject at a much deeper level than I think any AI is capable of at the present level of technology. But it would be passable to use it for a company name, to indicate that it is a goal to strive for.

Generally agree, though I would say "knowing a subject at a much deeper level than any LLM is capable of", as AI more broadly also includes specialist models that are wildly super-human in narrow domains like chess and Go.

They already have.

Grok is a word in common parlance. So there's no way they could succeed in any suit. That's why the Groq team picked a modification of the word.

You mean like Canvas®, Apple®, Windows® or Amazon®? Wanna try re-use these for your own business and see how it goes?

There's nothing preventing you to trademark common words, it just must not be descriptive of your business.