For most people in the action teams, having a public identity meant nothing more than trouble.
While they would have an identity prepared for them in case they needed to travel from one base to another, most of them would not bother to manage their identity. It's better to stay in the dark than to show their faces in front of the camera and so on.
Sagittarius was raised in the organization and didn't even have any public identity.
Leo himself had a public identity that he could use when he wanted to travel to other bases, but he rarely used it. Besides, some of his identities have been blacklisted, like the one that he used when he visited the Sun Country Base.
Arya didn't know the details but she remembered that Leo seemed to hate this base very much.