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.
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 companyname, 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.