If you want to register a new domain, which can be done through any registrar, you can put your identifier as a contact person. Your identifier is the name of your account you created through mojeID service. The identifier is put down without an extension .mojeid.cz, just namely (eg. Petra). If you already have a domain and you want to link it with your created mojeID account, you need to contact the domain registrar and make there a change of the holder. The Registrar will inform you what is needed to perform such a change.
Yes, it is possible by an identified account, it means PIN3 has been entered. You cannot hide the address by an account of a legal person.
You will hide it in Domain browser. Click on Domains up in your account and go the the Domain browser. Click on “My contact”, untick by address the item “Public” and save. The permanent address in the register will be hidden.