There aren't many suitable shortenings of this name. Although you can bet money that somebody will call her "asteroid" someday.
Famous people named Astrid:
Actress Astrid Allwyn; Olympic swimmer Astrid Strauss; musician/songwriter Astrid Williamson; children's novelist Astrid Lindgren; photographer Astrid Kirchherr.
Astrid Magnussen is the teenage main character of the Janet Fitch novel/movie White Oleander.