We work database first and moved the database to another server 2005 -> 2012 server

I can't find the possibility to change the server name. I tried to do that in the project XML file , only the name not the GUID, but that results in a complete reconfiguring.

What is the best approach?

Ok after changing the TargetDatabase GUID and ServerName it seems to work.

Rename the catalog in the catalog explorer, select it, F2->specify different name.

To specify a different server name when refreshing, simply connect to a different server in the connection parameters pane on the first step in the wizard. It's of course then required to have the catalog renamed to the new name as well, using F2 as stated above.