- Asterism (part of a constellation, like the Big Dipper)
- Squeaker (she made lots of squeaky sounds early on)
- Lovely Lady
- Little Bean
- Booger (more specifically, "My Booger" spoken exclusively by Kyra)
- Stink-topus (another name by Kyra)
- Id (Aster-Id, you know, since she's an Id...)
I'm not sure if the name Astrid and the root word aster- are related, but aster- means "star" (reference), which is close to the meaning of the name Astrid, "divine strength" or more paganly "heavenly strength". As noted on Wiktionary, Astrid is derived from an Old Norse name, Ástríðr. The name has two parts, either ást ("love, joy") or áss ("deity") and fríðr ("beautiful").
Astrid certainly is a "beautiful joy", that's for sure, no matter what we call her!
For a trip down memory lane, here's the same topic about Luca: Luca's Nicknames.