From what I could find out, the oud's name derives from the Arabic for "wood," just as the word "lute" does. The oud may have been so named either because of the strips of wood used to make its body or as a derogatory term relating to proscriptions of all instrumental music in early Islam. The wood used to make ouds is usually non-porous and hard but flexible, such as mahogany and rosewood.
Both agarwood and its resin distillate/extracts are known as Oud in Arabic (literally wood) and used to describe agarwood in nations and areas of Islamic faith. Western perfumers may also use agarwood essential oil under the name "oud" or "oude".