This chatroom is hosted on an IRC-Server,
all privacy questions and issues will be very similar to any other IRC chat network.
Every time you visit any webpage (or connect to any other server on the internet) you leave your
current IP address and your hostname as a footprint and it will show up in server logs. When you are
connected to an IRC chatserver, anybody can issue the /whois command and get your current
IP address.
Hiding part of your IP
To prevent other people from access to that detailed information the IRC server sets a special mode when you go into chat. This is done automatically and you don't have to do anything to switch it on. With this mode the server scrambles a relevant part of your IP address and hostname so it cannot be traced back to you. Although not all of the hostname is scrambled this mode adds a good chunk of privacy because it makes your connection untraceable for other chatters.
The first part of the hostname is scrambled (ez-4F5F1441), the hostname cannot be used to trace. The last part of the hostname is still unscrambled.

If you manually switch off this mode, the full hostname is visible to everybody.

IRC Bouncers
If you want total privacy for your chatting then you can use an IRC-Bouncer. Those are programs which are made just for IRC-ing and are hosted on a different server. When you connect through a bouncer, the server will only see the bouncer's IP and hostname, not even the server logs will show your true IP address - total privacy for chatting.
Most bouncers are hosted services and you will be charged a small fee to use them - use Google to search for "IRC bouncer" or check out XZibition and their bouncer service.
The use of a bouncer is not supported with the pre-configured web chatboxes on this site. You will need to set up an IRC chat client on your computer to connect to chat through a bouncer. If you need any help with that, chat to Moose in the room.