Which companions can I recruit into my crew?

You can recruit the following characters:

While I haven't yet completed the game, I believe that these are the only members you can recruit, due to in-game evidence:

Aside from the captain's room (yours), there are only 6 (initially sealed) rooms for crewmembers in The Unreliable. This suggests that you can only recruit a maximum of 6 crew members.
You may find special objects in Halcyon, which are used to decorate your crewmembers' rooms. You cannot choose how to decorate the rooms. They'll be automatically decorated as soon as you enter your ship with the decorations in your posession.
The rooms are decorated even if no crew member occupies it yet.
The rooms are decorated thematically. For instance, I found a Snake Skin and three animal Anatomy Posters. They all adorn the same wall of the same room, implying a biology or animal theme.
The rooms are decorated according to the crew members' theme. The animal-themed room described above ended up belonging to Nyoka, the huntress.
As soon as the room is occupied, you can examine its decorations. The Pteroray and Raptidon Anatomy Posters both offer a comment that directly references Nyoka by name.

Based on the above evidence, it is unlikely that you'll have to dismiss an existing companion to make room for another.

You can recruit 6 companions to your crew:

You can recruit all 6 of these characters, and none are mutually exclusive. (Source and walkthrough)

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