Cola, Grenadine, and Whiskey?!
Answers:
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In short: No.
In long: There are only about 30 drinks with "official" names, that is they're recognized by the IBA and similar drinks/bar associations with some credibility. Those are going to be your classic mixers and cocktails. Popular drinks like carbombs and Jager bombs and even call drinks like a 7&7 or redbull & vodka aren't going to be part of that list. So if you or anyone else cobbles some mix of liquors together, you can call it whatever you want. Restaurants and bars do it all the time with their house drinks. Just know that there's no real process to have it officially recognized and know that you can't really copyright a recipe that uses common ingredients.