Is there a name given to matrices of the form A'XA or AXA'? A is either symmetric or NOT.

Question

I understand that $x'Ax$ is generally called the quadratic form, with $x$ being a vector and $A$ is symmetric.

Is there a name given to matrices of the form $AXA$? $A$ is symmetric, and $X$ here is a matrix which may not be symmetric.

Edit:
Case 2: If $A$ is not symmetric and not an identity, is there a name given to any of the forms $A'XA$ or $AXA'$?