Starburst is her own filly. She is not bound by your societal labels.
Despite her status, Twilight wanted a normal upbringing for her daughter. She did not want her to grow spoiled or distant from others from withinin castle walls or prestigious scools. And so chose to raise her family in ponyville. Where the the mad, the mundane and the mighty mingle in a massive mix.
This desire for normalcy is one of the few things that her daughter agrees with her on.
Though titles and power in this world are earned rather then inherited, it does not stop ponies from recognizing the inheritance of the family name.
Its a recognition Starburst could do without, as she rather not live in the shadow of her mother's accomplishments. Or that of her older sister Nyx. Or her father Flash Sentry.
It's something that Blue here would learn the hard way. Colt sure did have an extensive vocabulary, even is this pre-buttmark, kindergarden years.
Starburst is based on the character of the same name by: Kianamai