You can't have a single datasource that will "work with any computer" - you need to address the specific instance of SQL server that hosts your database, and connect to that. Not only can the name of the PC it runs on be different, but the instance name does not have to be SQLEXPRESS either. Different installations will have different logins as well, so "Integrated Security" may not always be "SSPI".
If the user enters a server name, then just build the appropriate string from that - it's just a case of creating a formatted string from
string s = string.Format( "server={0};database = Holoo1; Integrated Security = SSPI", myTextBox.Text);
but you may need different security info as well.