Of course potatos have names...idaho, yukon, russetts, florida whites...tons of different potatos here in the U.S. and likely different varieties in europe because of growing climates and soil. They originated from south america and were took over to europe via spain by spanish explorers.
I know if i go to a restaurant and order home fries i get diced potatos not sliced and usually cooked with peppers and onions and much drier than my mom's fried potatoes which tend to have a little oil on the surface of the slices and not fried til dry.
My wife makes them that "dry" way.
There's a deli near me that makes homefries to order from frozen discs of potatoes that are deep fried. You can then ask to have them griddled with various veggies.
As far as names go, I wonderif South Americans have a name for each of their thousands of varieties?
I love some of the British names, though.
https://www.greatbritishchefs.com/features/potato-variety-guide