Well ... I'm back, with more information, but, so it seems, maybe the same problem. We've ditched that Kyocera printer and now we use two Lexmark's C792de printers. Now adding printers looks like this:

Remember, it's just two printers and I really don't think they're both defective. I there things are happening "by design", I just don't know enough about Bonjour to understand what's happening. It appears "Zero configuration name" can be changed via some action. First few lines from the picture above resulted in configuring the first printer while it already had access to the network. After certain configuration changes, zero configuration name changed automatically.
But the second printer was completely configured without the ethernet cable plugged in. But after a while, the second printer still became visible with "(2)". Something tells me, that after a while, I'll see (3) and so on.
By the way, those ~100 lines for Kyocera printer are still visible. Printer has been reconfigured with another IP address for a different network, with disabled Bonjour and is being used in another department. So what keeps these names "active"? I've read somewhere that disconnected devices dissappear "after a while". Couldn't find out how long this "while" lasts.
And it seems I'm not the only one who has similar problems: wireless printer multiplies in bonjour every 2 seconds
The owner of that Samsung printer has/had a bigger problem, maybe with similar cause. But at the end of that thread, user x5150 mentions he has multiple entries for the same printer, for every Mac user on the network. I doubt that these entries on our network are from Mac users, I would expect to see more entries than there currently are.
Are these entries shared by Mac computers that are connected to the network?