In complicated melees, I can't always remember which demigod is which based on the player name.  Often I know, e.g., that I want to pound on the Torchbearer a little more, but I can't remember which of the names is attached to him.

I have a few ideas that might help here:

1. This one should be pretty easy: attach the demigod's portrait to the box that pops up with their name, so I know who I'm pointing it.
2. Always show portraits and health bars for all demigods, with the light side on the left and the dark side on the right.  When the player mouses over a portrait, highlight the demigod on the field.  If a demigod is in the fog of war, gray out their portrait and the health bars.
3. Show (or have an option / keystroke to show) "floating" health bars for all the demigods currently on the screen.  I can't draw well enough to show this, but... what I'm thinking of is not just a bar right on top of the player (if I can't see them anyway, showing a bar that I also can't see does no good), but instead a system that would draw the bars somewhere on the screen that's reasonably clear, with a line pointing at the demigod it refers to.  Color-coding could indicate which side is which, although you'd also need text for colorblind users.  This is my favorite, but it seems complicated to implement; I know I've seen similar things in other games, though, so it's doable!  A handy extension would be to have a separate keystroke that does the same thing for defensive structures (popping up all their health bars at once).