penholder
/ˈpɛnˌhəʊldə/noun
A cylindrical rod or tube of wood, metal, plastic, etc., into which the nib of a pen may be fixed, and which then forms the handle of the pen. Also: any container or compartment for holding or storing a pen, especially a cylindrical tube, often on its own base, into which a pen may be inserted when not in use.
Origin
Early 19th century; earliest use found in Duke of Wellington (1769–1852), army officer and prime minister. From pen + holder.