Crab Rangoon has been on the menu of the "Polynesian-style" restaurant Trader Vic's in San Francisco since at least 1956. Although the appetizer is allegedly derived from an authentic Burmese recipe, the dish was probably invented in the United States. A "Rangoon crab a la Jack" was mentioned as a dish at a Hawaiian-style party in 1952, but without further detail, and so may or may not be the same thing.
In the Pacific Northwest states of the US crab Rangoon are also known as crab puffs, although this primarily refers to versions that use puff pastry as a wrapper instead of wonton. They may also be referred to as crab pillows, crab cheese wontons, or cheese wontons.