What to do when another company claims your name and logo?

Alright, put briefly; I just got an email from the CEO of a company claiming I copied their name and logo for my company, which I did not. I didn't even know of his company until his first email. This is very clear, the name is not the same as we have another ending, and their logo is not even half close to ours. The branding and industry are vastly different as well.

But, he's insisting and mentions he will bring his lawyers over the matter. This is not a case (yet), and I hope it remains this way.

I don't think it's fair to push a smaller company this way, especially not (essentially) threatening with legal action. But life isn't fair, and this is to be learned from in the future.

Either way, I'd like your input on the situation and what the best solution would be here?