In the upcoming BE 2.0, there's a way to disallow visitors who are not logged in from leaving comments. It's part of a new Rights system. Logged out users are part of the "Anonymous" role. You can assign or remove rights such
as "creating a comment" to the Anonymous role.
Even in a pre-BE 2.0 version without this Rights system, you can still modify BE to only allow logged in users to leave a comment. It's actually a couple of small modifications in CommentView.ascx.cs in the "User controls" folder.
In RaiseCallbackEvent(), add the highlighted part shown below
if (!BlogSettings.Instance.IsCommentsEnabled || !Page.User.Identity.IsAuthenticated)
.... and in the same file, in Page_Load, a similar change is needed:
if (BlogSettings.Instance.IsCommentsEnabled && Page.User.Identity.IsAuthenticated)
.......... for a different Membership system, maybe someone has already done something. BE uses the ASP.NET Membership provider system, which is actually flexible in that you can swap it out for a different membership system. BE has already actually
done this with the XmlMembershipProvider and DbMembershipProvider. You could create a new Membership system based off of the code in these providers ... and tailor it for your needs.