Barbie is sometimes depicted with brown hair; in this case, her name is still "Barbie." However, there are other dolls from the Barbie line of toys who have brown hair and are different characters with different names, such as Whitney and Teresa.
For example, there is a Barbie doll called "I Can Be Ballerina," which comes in a brown-haired version. This character is still Barbie. One doll that always had brown hair in all her versions is Whitney, a character created in 1987. The character Teresa is often described as Barbie's best friend and is often shown with brown hair. Other Barbie characters with brown hair include Tia, Kayla and Barbie's little sister, Skipper Roberts.