Donkey Kong got his name because its creator thought Donkey meant stupid in English.

Nintendo wanted to use the Popeye comics to make a game, but weren’t able to get the license for him. Because they couldn’t use Popeye, they decided to make new characters and Donkey Kong was born. Having done some development work on a Popeye game, they decided to create a love triangle between an ape, carpenter, and girlfriend, that looked sort of like the love triangle between Popeye, Bluto, and Olive Oyl. 

The game creator, Miyamoto, also used the Beauty and the Beast and King Kong as influences for his work with Donkey Kong. He came up with the name Donkey Kong because, not a fluent speaker of English, he thought that Donkey meant stupid. 

His intention was that English speakers would see the title Donkey Kong and see Stupid Ape, but he messed up. In Nintendo of America, Miyamoto was the butt of many jokes, but nevertheless the name stayed the same. 

The character Donkey Kong shows up in as Mario’s Enemy in his first game. He has also shown up in Mario Kart and Super Smash Bros. Donkey Kong is one of Nintendo’s most well-known characters. After being reformed sometime in the 90s, he's now counted amongst Nintendo's heroes.

(Source)