Sql Exception 0x80131904 cannot log in

My program connects to a MSSql database. If it connects via LAN it works fine, if it connects from outside I get the error message 0x80131904 Error when logging in the user 'ProgProj'. (translation might not be the same as on the english version. On the german version its like that)

I can exclude a port problem, because when the port was closed the message was that the server was not reachable. After opening the port it says it cannot login. But the login works on LAN with the very same Username and password.

What could be the cause of this problem? thanks!

EDIT-------------------------------------

It micht be that i have multiple databases running. When i connect via lan I set the servername and the name of the database. for example: sqlhost = DB01\DBNAME when i connect from outside tough, i do not specify what instance i want to connect to.. only the public IP address.. Because the ip addres followed by the \DBNAME does not work. how can i specify the server instance i want to connect to?