Yes, you have the option to make your domain details public or private in your dashboard after you've checked out. There is no charge for doing this! Ever since GDPR came into play in May 2018, we now automatically set any domain that is created or transferred to private, so none of your details are available via WhoIS! 

If you wanted to change this, simply login to your Dashboard, go to your Domain List & click the pencil to edit the domain. You can then click the privacy toggle & save your settings.