What is the name for the shape formed by removing a square from the corner of a larger square?

The name for the shape is gnomon. From Wikipedia:

The ancient Greek mathematician and astronomer Oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another. Later, the term was used for an L-shaped instrument like a steel square used to draw right angles. This shape may explain its use to describe a shape formed by cutting a smaller square from a larger one. Euclid extended the term to the plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive figurate numbers, including square and triangular numbers. The ancient Greek mathematician and engineer Hero of Alexandria defined a gnomon as that which, when added to an entity (number or shape), makes a new entity similar to the starting entity. In this sense Theon of Smyrna used it to describe a number which added to a polygonal number produces the next one of the same type. The most common use in this sense is an odd integer especially when seen as a figurate number between square numbers.

It's a gnomon. Euclid used it often. Here's an example from Book II, Proposition 6:

I usually call it "an L-shape". Most people would understand that, I think, and in the end that's what terminology is for: Not for discussing what's right and wrong to say, but for making yourself understood. Is that the actual word for it? I don't know. Does it really matter? I don't think so. If you feel uncertain, call it an L-shape, and give a brief description like you did here, or a drawing / figure, and you should be in the clear.