Every player has one Hero slot available from the get-go. Two additional slots can be unlocked by meeting certain requirements.
The second slot unlocks once you have recruited Ariadne as a Hero.
The third slot becomes available once you reach Celestial Boost Level 19 and have these boosts active.
Note that these slots need to be unlocked before the Preparation Phase ends if you want to bring two or even three Heroes into battle. Especially the level 19 Celestial Boost needs to be already active at the exact moment when the War starts. Unlocking and using the additional Hero Slots after the War has already started is not possible.