Incognito, available from Pearl, hides your profile from everyone’s Discover. The exception: if someone already liked you before you turned incognito on, they can still see and match with you.
Incognito only affects discovery. It does not hide you from the ship map or from port-overlap information for people you’ve already matched with. Those work the same whether incognito is on or off.
You can turn incognito on or off at any time in Settings.