No, the only way he can do this is if your company were to purchase the truck from him.
We don't loan our tools to the customers and we don't use their tools.
The same goes for employees.
It's a personal vehicle that does not belong to you.
It's not a commercial vehicle, it is neither registered nor insured as such.
Your company does not own it.
No, not unless he sells it to your company, tag, title, and all.