Windows 8 changed a bit compared to Windows 7 and Windows Vista. We all know that. It also changed the place, where you can choose what kind of network type you want to apply to the connection. Private, public, work or domain are no longer chosen via Network and Sharing Center.
Instead open the networks charm and right-click (or touch and hold) the network you want to change and select “Turn sharing on or off”.
Then choose the network type – it is an indirect choice. You no longer choose private or public directly, instead you choose the kind of sharing behavior the network should have.
As a final step you can verify that your selection is reflected in the right way using Control Panel\Network and Internet\Network and Sharing Center\Advanced sharing settings. Just look for the profile marked with “(current profile)”