Government is able to know the transactions you make when you’re making use of an exchange that is centralized. Centralized exchanges always make reports to the government, but decentralized exchanges has nothing to do with the government and they can never tell what’s happening on decentralized exchanges because they have no access to it and does not control it.

So, if you don’t want the activities you’re into in the crypto community to be known by the government, it would be best that you start making use of decentralized exchanges, if not, then you’re still exposed to them by using centralized ones.