Does the operator $A^*A$ have a name?

The self-adjoint operator $A^*A$ (for a generic linear operator $A$) is used in functional analysis, linear algebra, statistics, physics, and probably many other fields. I am curious if there is a standard way to refer to this operator? There's the Gramian of course, but that seems specifically to refer to a collection of finite-dimensional vectors. "Gram operator" seems natural to me, but Googling suggests that it's not widely used.

• Gilbert Strang loves to emphasize the importance of $A^* A$ in linear algebra, and I don't recall him having a name for it. (He also emphasizes $A^* C A$, where $C$ is symmetric positive definite.) Jan 21, 2017 at 21:19
• I have seen the notation $A^G=A^*A$ to emphasize this "Gramian" operation ... as an operator. Jan 21, 2017 at 21:27