The Family You Choose

You'll pick up a number of companions automatically (and optionally) as you progress the story.

To get more, go to bars and social areas in any of the cities and look at the random NPCs there. Some will have titles that align with roles on a ship - talk to them and they'll usually agree to join your crew.

Get 10 and the achievement will unlock. Note that you don't have to actually assign anyone to a role on your ship - just them being in the roster as a companion is enough.