BUILTIN\Administrators is the name of a User Group, not a Server. The name of your Server looks like its SQLEXPRESS, or maybe SYSTEM\SQLEXPRESS.

A User Group is, as the name suggests, a group of users. It enables you to assign privileges to a group and then every user you add to that group receives those privileges.

If you were using SQL Server Authentication, rather than Windows Authentication, then you'd put the name of one of your Users into the User Name field. if you wanted to log on with administrative privileges then you'd use one of the Users in the BUILTIN\Administrators group, which would include the 'sa' user.