It is the same term that would be applied to any Crow chief, male or female.

By combining it with the indicator of her being female, the name Bíawacheeitchish preserves the specific social fact that she was: someone recognized as a chief, in the full sense of that term, who was also a woman.

This is not a consolation title or an approximation.

It is the real term, combined with the descriptor that acknowledged the specific thing that made her case unusual.

The Crow gave her that name.