There are two types of captains for Dota 2 on FACEIT:
The FACEIT team captain
The FACEIT team captain doesn't have any particular roles in the match room.
The DOTA 2 team captain
The captain role can be claimed by any of your team members. The player who clicks the button first will be assigned captain.
Please keep in mind that usually the player who is chosen Captain in the match room is the most experienced and will give you the best opportunity to win the match as well.