Game > Commanders
When you are moving a commander to another base, they use a jump gate if there is one available. Note that you must de-assign a commander before moving them.
All names are randomly generated, but you can rename your Commanders.
Production Commanders do not increase directly your base production, it only reduces the production time, resulting in a indirect increase of the production capacity of the base.
You must assign commanders to be Base Commander of a base in order for their effect to take place.
It's just like demolishing structures or decommissioning fleet, though you do not gain any of your credits or XP back.