Is it correct to choose Rod's COM as origin of an inertial cordinate system?

The center of mass can be used as the origin from which to evaluate angular momentum, and torque, even if the center of mass is accelerating. The text by Symon, Mechanics, has a very complete discussion and derivation of the appropriate relationships.

To be more specific, the center of mass is chose as the origin for motion of an unconstrained body in space. If the body is constrained by some external forces to rotate about some fixed point $O$ (fixed in the inertial frame), that point is used for the origin. In both these cases, the forces and torques are those in the inertial frame. [If the fixed point for rotation $O$ (not the center of mass) is accelerating, then fictitious forces need to be considered.]

The details of this specific problem were not explained in the question. But if we choose the initial COM of the rod as the origin, the subsequent movement after the collision can be decomposed in translation of the rod COM + its spin around the COM.

The total angular momentum before and after the collision (including of course the ball), is conserved if calculated from that same point.

Choosing that origin has the advantage that $mathbf r_{com} times mathbf p_{com} = 0$, so the angular momentum of the rod is the value calculated from its COM.