You might be surprised to learn that in the trademark law, common words like "paper" or "candy" can be used by multiple companies without them infringing on each other while "Coca-Cola" is way too specific for that.
Because "Coca-Cola" is a "fanciful name", employing strange capitalization and hyphenation. It's also a household name world-wide, which allows protection of somewhat generic names.
It's a matter of common usage. Coca-Cola isn't a universal descriptor of that particular kind of carbonated soft drink. The term for that (in the US) is a cola (which is why there exists a lot of *-Cola beverages).
The Coca leaf isn't used anymore due to the prohibition of cocaine.
