If you are getting a traffic service from a civil controller then you will probably have a squawk. The MATZ controller can see your squawk and will know from the number which controller you are talking to and also your height.
I suggest this is sufficient, he knows how to contact you and the civilian controller can warn you of any military or other traffic. So no need for you to change frequency, not that it would do any harm but its not needed.
If like me you do not have a transponder then I would call the military just so that I can tell them my transit height as they cannot read this from the mode C.
ZA