Include Site Name In Notifications?

Suggestion: it would be useful if the notification e-mails also included the site name. I’m using it on a multisite install, & there seems to be no way to distinguish which site the login came from (i.e. one site is http://www.example.com, another is http://www.example.com/sub1 – but notifications always just say “www.example.com,” even when they came from the sub1 site).

Thanks!