I totally agree! Just been having this discussion on Reddit. It makes no sense to only save the main domain when it might have nothing to do with the page required to login.
Many of the names given for a Password URL are so generic that you can't tell what the password is for. I think the name should be editable so that you could definitely tell what the password is for. It's not an issue on all but some URL's are so cryptic you can't tell who it's for without clicking on it to see and even some URL's you can't tell till you login. Thanks for considering.