How long before the Groq team sues for trademark violation? It's literally the purpose of trademark laws to make sure resembling names do not cause confusion in the mind of customers so it would be very surprising to see this situation persist.
There's nothing preventing you to trademark common words, it just must not be descriptive of your business.
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.
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.