Of course they will. Every centralized exchange does it and does it regularly. If a government comes along and says "Hand over the information of all the citizens from our country using your platform or we will ban you from operating here", then every exchange will comply immediately to safeguard their own profits. Coinbase do it. Binance do it. Kraken do it. They all do it.

You should assume that any and all information you give to a centralized exchange can and will end up in the hands of various governments and associated agencies.