Everest is a city in Brown County, Kansas, United States. As of the 2020 census, the population of the city was 265. Everest got its start circa …Everest is a city in Brown County, Kansas, United States. As of the 2020 census, the population of the city was 265. Everest got its start circa 1882 following construction of the railroad through that territory. It was named in honor of Colonel Aaron S. Everest, an attorney for the Central Branch Union Pacific Railroad who represented Atchison County in the Kansas Senate.