What is the top of a door frame called?

Answer 1

The part of the frame across the top of a door is called a lintel if it is structural (bearing a load). If it is not structural, it can be called a head trimmer. The headis the top of the door.

Answer 2

Threshold. Or a sill

Or Soleplate. DOOR SILL as opposed to the term WINDOW SILL. OR DOOR STEP. A Soleplate is more correctly, the piece of timber (usually about 50mmthick) placed in the soil and beneath a timber or concrete Stump of a house. It is typically 200 x 300mm and made from Red Gum or Jarrah so that it lasts a long time in the damp ground.

(USA answer) The bottom of a door frame is usually called the threshold or doorsill. A sole plate is the first piece of wood that lays flat on its widest face at the bottom of a stud wall. Studs (usually 2x4's or 2x6's) rest vertically on the sole plate. It may be made of pressure treated wood to prevent decay or a specie that resists decay naturally such as cedar, or cypress, or redwood. Corrected in this answer: The plate that rests on top of a foundation wall is called the sill plate (not sole plate).