Thanks for pointing me in the right direction.
Yes, the PS1 is part of OS X as well. If I do a echo $PS1 on one of the Macs, I get:
\h:\W \u\$
According to an Apple manual page, this should - in short - be read out as:
host\ basename of current wd ("~" if the home directory) \ user name of current user \ effective UID
(See
Mac OS X Manual Page For bash(1) under "Prompting"...)
If I apply this to what I have seen so far (see my initial post), it tells me that everytime I log one of the Macs onto the network, another client machine becomes the host of that Mac.
So, is this interpretation correct? And how could this happen? Since nobody has (or should have at least) made such settings to the machines, i e nobody has (or should have) set these Macs to become automatically "hosted" by other clients on the network upon logging on...
Also, as a sidenote, we have four Macs on the network; this phenomenon only occurs on two of them, the prompts of the other two remain unaffected whether logged on to the network or not.