This is about all of the information about legacy i know
You obtain your legacy name at the end of Chapter 1 (around lvl 3x if you do all the quests on the planets you go through). You create your legacy name by hitting y and then typing in the name and hitting accept (you can not change your legacy name at the current time).
You can level Legacy up by just doing quests and killing mobs. you can purchace various items (an astromech droid for your ship to buy legacy items, race unlocks and other things). You can also unlock some Legacy Skills (Force Choke, Orbital Strike, a dash from the bounty hunter, etc). You can only use Legacy Skills when you are using your Heroic Moment.