Plants in the same Family can be difficult to separate, usually a genus name has been given by a person who discovered it in the first place and that was likely in the 1800's or earlier. Another person might have found the same plant but thought it was different so gave it a different name only to be found later it's the same as an already named plant, and that's often why there's so many synonyms given. They used to have only physical characters to go by, now there's a lot of DNA testing going on so some plants are separated into a different genus, or put in the same genus when they originally had different genera names. It may well be that some which have a different genus name are actually in the same genus but someone has to get around to proper testing and that doesn't often happen.
There are organisations who get their heads together, such as Kew, MOBOT, Tropicos. look at the organisations on the Plant List. Even so, they don't always agree! Human nature plays a big role.
If someone has developed a new cultivar then they can register it and give it a name, this is usually only done by breeders in the business. Most species have already been found and evaluated, but there is still more species being found in remote areas of places such as Papua New Guinea.
That's a high NPK fertiliser you are using! Potatoes would love it. A high Nitrogen content will give lots of leaf growth, and a good dark green colour, Phosphorus and Potassium are for flower and root development. Some plants wouldn't do well with such high levels but yours seem to like it.