A two-headed bear is the symbol of the New California Republic.
A two-headed bear has never been depicted in the Fallout universe outside of the NCR flag. It can be seen as a metaphor for the NCR's founding in a post-War wasteland, home to a variety of mutated life forms, including the two-headed brahmin.
The only mutated bears actually seen in the Fallout universe, known as yao guai, appear throughout the Capital Wasteland in Fallout 3 and the Fallout: New Vegas add-on Honest Hearts, in Zion Canyon.
Appearances
A two-headed bear has not appeared in any Fallout game, but can be seen on the flag of the New California Republic that appears in Fallout 2 and Fallout: New Vegas.