No, you don’t need a suppressor license for each gun. Suppressors are classified as Title II firearms, and as such, they fall under the National Firearms Act (NFA). The regulations governing NFA firearms are found in Title 27 of the United States Code (USC), and they are administered by the Bureau of Alcohol, Tobacco, Firearms, and Explosives (BATFE).
To possess a suppressor, you must first complete an ATF Form 4 and submit it to BATFE along with a $200 tax stamp. Once your Form 4 is approved, you can then legally possess the suppressor. If you want to transfer a suppressor to someone else, you must complete an ATF Form 5 and submit it to BATFE along with a $200 tax stamp.
You can find more information about the process of purchasing and transferring suppressors in our article How to Buy a Gun Silencer.