Starfaring Companions are an aesthetic addition to your Trailblazer Profile. They don’t do anything. The option is there for you to show off your favorite characters. Many players will likely use this to show off their favorites. Some other may use it to show off their rare pulls or most powerful characters.
You can see your friends’ Starfaring Companions when viewing their Trailblazer Profiles from your friends list. They, and others, will be ablet to see yours as well. Otherwise, that’s really it for Starfaring Companions. It’s just a bit of glam for your profile.