Uh... this is actually pretty close to how things already are. At least if I'm interpreting this correctly.
When you have new notifications, it'll display the number of new notifications you have, and then the pull down list with links to them. (For example 3 notifications, and beneath, 2 PM's and 1 VM.) I don't think implementing the name into the PM/VM thing is possible with the forum software, but I really don't see the need for such a small change. You already know you have a message, and it would only take one more click to see who it's from.
As for Subscriptions, they aren't displayed in the Notifications tab, as you may have noticed (though there was talk in this forum of maybe putting them there, but such a thing was never implemented). However, if you want email notifications for your subscriptions so that you don't have to keep checking your subscription list, then that also already exists. You can select subscriptions by checking the corresponding boxes on the right of the list, and if you scroll down, there should be a pull-down list on the bottom that should allow you to change their notification type to "instant notification by email", which is exactly what it sounds like. You can also subscribe to threads by email when you first subscribe to them in the first place, since they should give you the option on the confirmation screen. Be careful, though, because for some reason, double-posting on a thread (in the way that causes your posts to merge) turns email notifying subscriptions into CP only subscriptions. Really any thread you double-post on will be listed in your subscriptions under CP only notification, regardless of whether or not you subscribed to them yourself. Really it's just a glitch, and any subscriptions you get this way can easily be changed back to instant email notifications, or downright removed.
There's also an option to get email notifications for PM's. It should be in your General Settings, I think.