You are a superhero just like your father and your older brother, when you started to get your powers or being trained as a superhero it came at a young age. When it comes to what you will be called it was up to you and the justice league to decide, along with the public trying to say your superhero name.
Batman
You are called the nightingale with the rest of your brother superhero names being birds , so you decided to be named after a bird as well and you came up with the nightingale due to your love for the bird.
Superman
You are called impossible gal because everyone in your family is called super something and after, thinking about it for three days you came up with the name impossible gal and your father and brothers like it.
Wondrous man
You are call ancient angel being the daughter of man raised in ancient lifestyles it was easy to come up with your superhero name, you were going to ancient princess but it was soon switched to ancient angel after you were called angel after saving a few people.
Green lantern
Green lantern gal being part of the green lantern core you name was green lantern but your father and uncles didn't want the public to know you name or any members of the core, that didn't know you were already live so you were called green lantern gal and you liked the name.
Aqua man
You are called serine gal the reason you are called serine gal was because a few fishermen and reporters thought you looked like a serine, you really didn't hate them for saying that to you but your father,brother, and uncle hated the idea but you said it was okay with you.
Flash
You are call swift gal you had the same speed powers of your father and brother, the name flash was already been used to many times so you were called swift gal. After you were complement on how swift you were when it come to saving people's lives.