Hi,
My preference would be to have the icons and names 'under' everything that moves or is created during play.
If I wanted to see the icon/name I could hover the mouse over them for a couple moments and bring them to the 'top'.
That way I can see everything on the map board.
Issue:
Think of a star system with several planets as colony/core worlds. Add in a few star bases and ship yards, now add fleets and loose ships from two or more players. Try to track every thing going on under the icons and names, very annoying. Monsters and pirates start sneaking in, etc.
Or just give me a way to turn off the icons and planet names. Have a hot key assigned to the option also to make it easy to turn on/off several times during a turn if desired.