If you want to get pedantic and lord noes you always do - They were more so called door cards when they were made out of masonite (masonite is a manufactured form of carboard that is a lot stronger and thicker than what you think of as cardboard - pressed fibers) hence the term Door CARD - later in production with injection moulding etc and plasticisation of it all they would start to be know as door trims - It helped in the past also when chrome was a big feature on the outside of cars and the door trim would normally be referring to the chrome pieces on the outside of the door.