Our organization was also a little bummed with the limited email notification functionality. In the meantime, I thought I'd share a tiny workaround to this for everyone else.
The notification name is included as the email subject line, so I've created around 5 different notifications so far with different names so I can tell at a glance in my inbox what has happened.
In my email, I see the following:
100% not ideal but at least I can at a glance know what the alert is for. Probably only good for smaller deployments like mine, unless you're okay with managing a bunch of these notifications. Hopefully we see this functionality fleshed out a bit in future updates. I'll probably keep doing it this way in the meantime..