No. That would be akin to banning anyone from calling something *cheese*. Cola is a family of drinks, of which there are many types and brands. Protecting the Parmesan part of Parmesan Cheese is the same as protecting the Coca part of Coca Cola.
Bad analogy all around since a corporate brand is being compared to a regional style.
A better comparison would be American Cheese...excuse me I think I have to puke just thinking about it.