I think this would be a lot work to implement because of the way procedural generation works (during hyperjumping irrc). But I may be wrong, it would be a super cool feature.
The info needed for the energy distribution of local stars is already displayed on the background sky itself, which is part of the reason we have a loading screen. The sky isn't proc gen. It's literally generated from info from the existing galaxy map (distance, color temp, star class, luminosity) all of these dimensions are the direct result of the energy distribution and should include info about the name of the star itself in the existing database. So the energy distribution is already included every time you jump to a new system, it's just represented as a beautiful sky.
Beyond being a cool feature, people have requested a feature to help ID stars you see in the background sky to aid in travelling there. Currently if you see an interesting looking star or star pattern, you have to try to line up your position on the galmap with the night sky relative to certain nebula, or the center of the galaxy etc. It's very wonky and works less than half the time for me because the perspective is always well off center.
Beyond the programming of linking up the existing data with the skymap, it might take an extra second or two to jump to a new system in order to load the relevant data of visible stars. I am guessing this because simply loading in double the number of stars (or the equivalent data) by changing the ini settings, only increases loading times by a blip of a second.