Does the transformation $(A\otimes A)B(A\otimes A)^{-1}$ have a name?

Question

If $B$ is a $n^2\times n^2$ complex valued matrix and $A$ is a nonsingular $n\times n$ complex valued matrix then define the transformation: $$B_{new}=(A\otimes A)B(A\otimes A)^{-1}$$

I'm wondering if this kind of transformation has a name and if there are any known properties.