B should have been served with the Complaint, which would also have a Civil Cover Sheet detailing the nature of the case and the time in which B has to respond. There is no court date set until AFTER the Complaint has been answered or the deadline to answer has (without an answer being filed) has passed. If an Answer has not been filed before the deadline, the court will enter a default judgment against person B, which is something you never want to have happen.
If A does not know where B is to serve them, A may take out an ad in the Legal Ads section of the newspaper stating that B has been sued and needs to head to the courthouse to get served with the suit (most of the time, the ads are required to run for a month or so). Most of the time, people don't read the legal ads, so generally speaking, B people never see the ad, never know they have been sued, and get a default judgment entered against them.
If you suspect you are going to be sued, keep your eye on the newspaper!
Not a lawyer, but work in the legal field 11+ years