No. How will users find your site if its IP is not public? DNS services have to be told where your site is hosted and the IP address does that exactly. http://www.howstuffworks.com/dns.htm
Yes, I know that. But, for example this website don't get any IP or server, but exist.http://www.moi.gov.mk Ca you explain this how they do that?
Every website name is mapped to an IP address. These mappings are stored into DNS servers so when a request comes for any website, DNS server returns redirects the request to mapped IP address. Without any IP address, website will not exist to put it in simple way. There is no way you can hide your website IP address. In fact, this is a MUST.
Yes I know that, but I was talking for that website how they do that. When You search WHOIS or WHAT IP is you don't get anything. http://www.moi.gov.mk
As others have said, the IP cannot be hidden if you want a working website and the linked website does have an IP as already illustrated. As to the WhoIs information, this will depend on a combination of 1) the TLD in question and 2) Who you are. For example for the UK TLD if you are a private individual you can elect to have most the information not shown in WhoIs queries (if you are a Sole Trader you cannot chose this option). I have no idea of the Macedonian rules for their Government and WhoIs but it seems to be that they aren't required to display it. You also need to ensure that the whois tool you are using does cover the TLD you are searching for otherwise you may get a false negative
Unless you have a second domain that loads the pages from your first domain (acting as a proxy)... That could work maybe... But you still then have to have ownership of the second domain..