If you are going to have the truck for 30 days or more then you have to put your DOT# and business name on the truck. That's what I was told by CA. DOT last year.
Where are you at? When I rent a truck, I have to put my numbers in it to legally cover the load because the rental company isn't the company with the operating authority.
I know a big equipment rental outfit here got in a big time jam, over a long term rental truck they had rented out and still running the rental numbers when it was wrecked. From what i got out of it, short term the rentals numbers, long term, numbers have to be changed. But don't take that as gospel,