Is it permissible for some girls to distinguish themselves by a specific dress (such as a white hijab) from other girls, with the aim of showing their religious commitment, and is it permissible for religiously observant women to wear a special uniform?

If the customary hijab in your country fulfills the Shariah conditions, then conform to the common practice of the people regarding it, and it is disliked to go against it. It may even become forbidden if the clothing reaches the level of ostentation (shuhrah). The white color for a woman's hijab has no special religious merit, so it should be left to conform to custom.