How long has the system been running ... the static information (name etc) is only sent every 6 minutes, so if you miss one you will have to wait a while before it gets sent again.
There's a couple of reasons I can think of that you might be missing the class B signals ...
There is limited bandwidth to the AIS
system, so in a very crowded area, class A signals get priority, making it harder for class B signals to get through. There is nothing to stop class B units "fighting" for the same transmission
timeslot, so in a very busy area they may be interfering with each other. Class B signals operate in the gaps left behind by the class A signals, but if a class B unit isn't receiving distant class A signals that you are receiving, then it may try to transmit at the same time thinking that there is a gap there.
The new class B+ units solve most of these problems ... but as long as you are receiving the position reports, then you've got what is most important ... but remember that in crowded conditions, although these are updated every 30 seconds, these too could be minutes old.
Edit: another possibility ... if the Plotter has limited memory for storing ships names, in a crowded area, it may prioritise the class A data when it runs out of memory.