Yes, you can do this if your account has been identified, meaning PIN3 has been entered. The only exception is the account of a legal person, where the address cannot be hidden.
Do the settings to hide your address inside the Domain browser, which is at https://www.domenovyprohlizec.cz/. Inside the Domain browser, click on “My contact”, uncheck “Public” option and save. That's it, the permanent address will be hidden in the register.