Make sure that the SQL Server Browser Service is running. Named instances run on a different port than the default instance (usually a dynamic port unless you changed the setting), the Browser service is what allows your client to connect to the name without using an explicit port number.
You can also try connecting by specifying the port number directly, this will bypass the need for the Browser service. Check the SQL Server errorlog of the named instance to determine the port the instance is listening on, then try connecting to servername,portnumber from your client.
If the above doesn't work, check to make sure that Windows Firewall (or any other firewall you may be passing through) is configured to allow SQL traffic on both the server and the client. It's possible that it's configured only to allow traffic on port 1433 which allows the default instance to work correctly, but not the named instance.