Pregnancy is 3 days whether you're playing the sim or not. If you want to be with the sim when they give birth, make sure you're playing them 3 days after they conceive.
(If the issue is they're conceiving on their own via a mod or Neighborhood Stories, either adjust those settings so they can't any longer, or use the notifications to keep track and switch to the family in time. Like with Neighborhood Stories you can click on the mailbox to see what changes have happened since the last time you checked, and it will tell you if a family is getting ready for their baby to be born.)
Yeah, it's annoying that newborns are objects and can't be renamed or moved to another house! You can change the name and move house after aging the newborn up into an infant.