The Fat Neils are a community to the northeast of Fort Kohai. They have constant issues with the neighbouring community, McCoys. You could recruit them after triggering their war with the Mccoys and they survive, which could be done by doing the quests Tit for Tat and Eye for an eye before making the two groups negotiate.
|“||The first group is made up of former employees of a Fat Neil's Fried Chicken restaurant. Talk to their leader, Dorcas Longabaugh, tell her I sent you, try to convince her to negotiate.||”|
— Wyatt Ingalis, from Fort Kohai
Several times throughout the game, the Fat Neils are referred to as Fat Neil's. It is possible that this could be the proper use of the name, and Fat Neils is rather an informal version of it.
The Fat Neils and McCoys conflict was inspired by the Hatfields and McCoys feud. Fat Neils being a play on the word Hatfield.