when you play household time passes for all the households in the save not just the one you are playing naturally then in 3 days time the pregnant sim gives birth regardless of if they are played or not
as for names though i think you can change it once baby is infant and you can take them to cas
can't remember if cas fulleditmode cheat is needed for names tho
the way to avoid this all is really to just play the household until baby is born and switch household only after it
and yeah if its neighborhood stories babies then toggle neighborhood stories off in household management as that is just another level of baby chaos