Well, not really hence tequila. Tequila is distilled agave juice, champagne is a white wine.

Sparkling white wine

Actually, the Champagne region of France is one of two places in the world with the legal right to call their sparkling white wines "Champagne". The other is California, due to California's wine producers buying rights to call their sparkling white wines "Champagne".
The first of the examples you mentioned is an attempt at a concept called "genericization", the process by which words that were originally copyrighted or trademarked become available for use by all manufacturers of nearly identical products. Had the word Kleenex become genericized, all manufacturers of facial tissues would be able to market their products as "Kleenex" despite not owning the rights to call their product such.
The second two aren't as much examples of anything other than people being extremely picky. Port and Parmesan cheese aren't trademarked or copyrighted terms, nor were they ever such. They are simply specific varieties of wine and cheese. It's important to differentiate between varieties of such varied products as wine and cheese. For example, if we had no names for different cheeses, some idiot would put Parmesan on a pizza instead of mozzarella.
The final one is one I've never heard of. Must be a regional thing.
The more you know.

actually Portugal does have the rights to port wine, thats why the only wine labeled 'port' comes from Portugal, otherwise its called 'fortified red'. and although Parmesan does not have the rights to the cheese yet, last i heard they are going through the works to get it done, i think they sued the company 'Kraft' about it. and you should really check out Nanimo bars, kuz they're fuckin amazing
anyways... moo point. because like i said, just because companies or countries trademarked it does not mean that people use the words for the specific regions, they use the generalizations of the words