I don’t know if you’re being sarcastic, but trademarking a famous scientist’s name seems legally dubious at best. Is that allowed? I.e. Tesla the car company and nvidia Tesla’s GPUs; is there a gentleman’s agreement between these two or is such a name simply not trademarkable?
In general a trademark is registered for a specific class (~industry). As long as the trademarks are for different classes and there is no risk of confusion, multiple companies/products can have the same name. For example Delta is the name of an airline, a computer company, a faucet company and a family of orbital rockets. There's little risk anybody would confuse these four, and they don't belong to the same class, so they can coexist just fine.
The US is quite generous in what you can trademark. In the EU for example you can't (as easily) trademark common words. But a quick search shows about 50 active EU trademarks on the word Tesla.
My understanding (IANAL) is that "Tesla" is trademarked by the company. [1] Note that doesn't mean no one else can ever use that name for anything. It does mean I'd probably get a cease and desist letter if I tried to go into the car business under the name Tesla. But I can probably get a trademark in other areas where there isn't a serious possibility of confusion. How close I'm willing to get to that line probably depends on how badly I want the name and how conservative the lawyers are.
Not sure why this is being downvoted because it's a good point.
Ampere, Ampere Semiconductor and Ampere Computing are all registered trademarks of the computing company in the class NVidia would need, and they'd have a good case this this is causing confusion (they'd probably cite this thread).