What is the name of the crust that covers both top and bottom of the pie?

The crust that covers both the top and bottom of a pie is called a double crust.

A double-crust pie has pastry beneath the filling and another pastry layer above it. The bottom crust supports the filling and helps form the pie’s shell, while the top crust encloses the fruit and allows steam to escape through slits or decorative vents.

The upper layer can be solid, scored, or arranged as a lattice. A lattice crust is therefore one possible style of top crust, not the general name for a pie with pastry on both sides. By contrast, a single-crust pie has pastry on only one side, usually the bottom.

Apple pie is commonly made as a double-crust pie, although not every apple dessert follows that pattern. Dutch apple pie may have a crumb topping, and French tarte Tatin is baked with pastry on top before being inverted for serving. These variations explain why “double crust” describes the structure rather than a particular decoration.