No process is on the other end of the pipe (SQL Server 2012)

The server was set to Windows Authentication only by default. There isn’t any notification, that the origin of the errors is that, so it’s hard to figure it out. The SQL Management studio does not warn you, even if you create a user with SQL Authentication only.

So the answer is: Switch from Windows to SQL Authentication:

1. Right click on the server name and select properties;
2. Select security tab;
3. Enable the SQL Server and Windows Authentication mode;
4. Restart the SQL Server service.

You can now connect with your login/password.

Here are the directions by Microsoft: https://learn.microsoft.com/en-us/sql/database-engine/configure-windows/change-server-authentication-mode?view=sql-server-ver15