There is a constant buzzing sound in the freezer door of my Kenmore refrigerator Model Number 363.9534720. The buzz sound stops when I open the freezer door but starts up when I close the door. Everything else is working properly.

What can I do to stop the buzzing sound?

These are the things to check.

https://www.repairclinic.com/RepairHelp/How-To-Fix-A-Refrigerator/56--503606-/new/Refrigerator-is-noisy-or-loud-3639534720

See all 5 causes and it could be as simple as a loose mounting screw for the fan motors.

Also consider these articles
https://www.subzero-wolf.com/assistance/answers/refrigerator-or-freezer-noises

Contains a few useful links.

https://www.subzero-wolf.com/assistance/answers/noise-from-compressor-area?kmref=K47909344

https://homeguides.sfgate.com/freezer-humming-noise-94649.html

Is there a frost build up by chance? Even plastic can freeze, and motors also. In that case a defrost may be your solution.