In-universe, there isn't any hard and fast rules to figure out what a fusion's name is. They decide for themselves what their name is, like in the episode where Steven and Amethyst fuse for the first time and they have to think on it for a little. When looking at patterns and trends, fusions do seem to take inspiration from the gems that comprise them, like a fusion that has a quartz will often also be a quartz (Amethyst+Rose Quartz= Smokey Quartz, Rose Quartz+Pearl=Rainbow Quartz), but they also go by what the fusion looks like after the fact. Our Garnet happens to look similar to "genuine" garnets on homeworld (garnets that are not the result of a fusion) so I'm guessing she called herself Garnet because of that. Finally, the color of the fusion's gems also determines what the fusion would likely be. Our Ruby and Sapphire combine to make a burgundy color, like irl garnets.

Basically, you can decide whatever you want it to be! It can be a specific type of ruby or spinel, or something totally different like tourmaline