If their host displays as a customs line, so without any TLD (like .com .net .org) at the end, then the IRC network offers virtual hosts, or vhosts.
As mentioned above, you should ask about this in the network's help channel.
If the hosts *do* end in a TLD then those people are using bouncers, or BNCs. Basically these are paid-for services you can use to anonymously connect, for instance, to an IRC server.