This section of Call of Duty Cold War guide will help you deal with hiding bodies in stealth missions. Thanks to this page of the guide, no one will find the bodies of incapacitated enemies and you will be able to complete a mission without raising an alarm.
In stealth missions, getting rid of enemies is not always enough. The bodies must be disposed of so that no alarm is raised and no guards can detect them.
After eliminating an enemy, you will be able to pick them up (by default, by pressing F, the action key). However, be careful, because you'll be slower while carrying the body. Once you're carrying the body, the game itself will show you where you can hide it, showing you these spots as mission objectives. It will always be closets (with the exception of the Brick in the Wall mission, where it will be a couch). Get closer to the closet and press the action key to hide the body. Problem solved, you can move on.