Don’t know that the letters stand for anything. K was invented by, I think, a Hoskins company, and it uses “chromel” and “alumel”. Perhaps somebody called it “kromel” as a cutsey trade name? N is Nicrosil and Nisil, so maybe those are related - but I don’t know which got named first, the type or the alloys. E has the largest "e"lectromotive force of any of the common ones. But these are all just guesses, and I sort of doubt they’re right.
K, J, T, and E are the most commonly encountered base-metal thermocouple types, with K and J being the most common of these. I like type K. I think type J sucks. T is often used at cold temperatures, since it’s the only thermocouple type where limits of error have been assigned for T < 0 °C. Type T is also a good choice for thermopile (differential) setups. Type E is often used in research, since its high sensitivity can be easily read with a nanovoltmeter.
I’ve used type W thermocouples in a vacuum furnace. They’re very difficult to work with, and a real bitch to weld.
Types S, B, and R are “noble metal” thermocouples. Because they use platinum alloys they’re very expensive per inch. Type S is commonly used as an interpolation standard for calibration purposes. Type B is cool… it’s the only thermocouple type that doesn’t need a reference junction. Just hook up a nanovoltmeter and take a reading.