It is the engine splash shield or lower engine cover - I really don't know VW's name for it. Anyway, it is a pain. Unless you use an oil evacuator, the splash shield needs to be removed for each oil change. It is very common for the oil change mechanics to not put all the fasteners in correctly. There are 9 quick release pins and a metric nut that hold it in place. The fasteners fall out, the shield drops a little, then the airflow under the car rips it to pieces. You are not alone. If you do a search for the terms above you will find multiple posts about cars that have had this problem.
Unfortunately you can't take it off the car because it connects to the wheel well liners. If you remove the splash shield, the liners get blown into the front tires and quickly have holes worn into them. My suggestion is to become very familiar with how the shield attaches to the car. Either buy some spare OEM fasteners to have on hand or get some zip ties to use in place of them. Every time you have the oil changed, check that the fasteners are correctly installed before leaving the shop.
It is such a pain. Welcome to Passat ownership.