A question to the OP: Can you share the name of the business your friend runs? Not all businesses with "DeLorean" in their name infringe on DMC rights but some might.
DMC has the right and even the duty to police its intellectual property including a trademark or trade name. Without licensing or restricting the use by third parties DMC risks dilution of their mark or name. Eventually the mark or name can become unenforceable because it's essentially been abandoned by its owner.
At the same time folks who want to do business selling DeLorean parts/service or privately renting their D, even with some reference to a DeLorean, can do so freely as long as they follow the rules. Make sure the business name is clear of confusion with DMC's name or ask DMC if they're OK with a current or planned name for a business.
As David T says, Disney and others are very protective. So are the automotive OEMs.
As for our vendor community it is presumably not a problem. DPI, now known as DeLorean Industries, has a
nice disclaimer, for example. Other vendors may be using business and product names that don't infringe on DMC.