What is the name of the female bat character in Sonic?

The female bat character in Sonic is Rouge the Bat.

Rouge debuted in Sonic Adventure 2 (2001) as a treasure hunter searching for valuable jewels, especially the scattered pieces of the Master Emerald. She later became a part-time government spy working with G.U.N., and often operates alongside Shadow the Hedgehog and E-123 Omega as part of Team Dark.

Rouge is a playable character in several Sonic games. Her main abilities include flying with her wings and attacking with powerful kicks, including her signature Screw Kick. Her treasure-hunting role also creates a deliberate rivalry with Knuckles, who is the Master Emerald's guardian.

A common mix-up is confusing Rouge with Amy Rose, another prominent female Sonic character, or with Cream the Rabbit. Rouge is specifically the franchise's white anthropomorphic bat, while Blaze the Cat is a separate character from another dimension.