The center of mass does not depend on the axis of rotation which is chosen. The center of mass is the point at which the mass of an object is concentrated, and it is determined solely by the distribution of the object's mass. The center of mass is a fixed point in space for a given object, and its position does not change with the choice of axis of rotation.
However, the choice of axis of rotation can affect the moment of inertia of an object. The moment of inertia is a measure of an object's resistance to rotational motion, and it depends on both the distribution of mass and the choice of axis of rotation. Different choices of axis of rotation can result in different values of moment of inertia for the same object.