Robert Buckley, as far as I know, there isn't a way to customize the header in the way you're specifying. Dashboards allow for some customization using HTML, but that option doesn't seem to be available for every dashboard element.
I feel that having additional customization capabilities within Dashboards would be a huge improvement (both through rich text editors within the WYSIWYG or something similar to Web AppBuilder Developer Edition). You can check out the ArcGIS Ideas page to support this and other enhancements you'd like to see in the platform.
I did find this idea. Kevin MacLeod commented about "Dashboard for Portal", which I don't have experience with. Maybe it allows this kind of customization?
Operations Dashboard Developer Edition
Derek Law (Dashboard guru), any insight?
Best,
Katie
“The goal is not simply to ‘work hard, play hard.’ The goal is to make our work and our play indistinguishable.”
- Simon Sinek