When I first started learning about chemistry, I played many of the same word games--every field in science has its own language, and way of communicating ideas. Chemistry, in particular, has worked hard for over a hundred years trying to systemize chemical names so that concepts can be clearly communicated among the academic community. The major thrust of this effort is the International Union for Pure and Applied Chemistry (IUPAC), which has been working to standardize chemical terms since 1919.

The naming of ionic compounds follows the rules you're alluding to in your question. But that's not the only naming convention around! When we talk about the chemistry of carbon-- organic chemistry we use a different set of names to simplify our communications.

Moreover, carbon is rarely stable as an ion-- with a positive or negative charge. Very unique chemical structures exist to generate carbanions (negative carbons) and carbocat ions (positive carbons). But when two carbons interact,they almost always do so in a covalent bonding fashion, forming long-term bonds together, rather than through electrostatics (positive and negative ion interactions).

Carbon is usually found bound to 4 hydrogens, CH₄. In organic chemistry, this is called methane. If two methanes combine, two hydrogen atoms will be released, leaving C₂H_{4
Hope that answers your question!}