What are the names of fiesta servers

I assume you mean Fiesta Ware serving pieces. Fiesta Ware was manufactured by the Homer Laughlin Company, from the 1930s until mid-1970. The company now makes and sells Fiesta Ware in new colors to distinguish pieces from the original stuff. This website shows the various pieces and their http://www.hlchina.com/fiestaitems.htmnames: