Atlantic: 4-4-2 - A 4-4-2 built in 1896 for the Atlantic City Railroad gave the wheel arrangement its name.
Pacific: “Mystery surrounds the origin of the name. One theory holds that the 4-6-2 earned the name Pacific when some locomotives of this wheel arrangement were shipped across the Pacific to New Zealand. Another suggests that the source is the Missouri Pacific following delivery of a batch of 4-6-2’s to that railroad in 1902.”
Mikado: 2-8-2 The first of these were built by Baldwin in 1897 for Japan; hence the name.
Mountain: 4-8-2 named for the locomotives supplied to the mountain-climbing C&O by Alco in 1911
Source - Classic North American Steam - Huxtable