I assume a lot of streamers wish to keep their IP address private and also IP addresses for servers and what not. This is just a simple solution that I assume a lot of people know about but not everyone (note: this tutorial modify's a system file on Windows operating systems so make sure you have Administrator access otherwise efforts will be futile). You should also note this tutorial is only for Window based systems (XP - W7 [I assume also W8]).
Go to Start > Computer > Main Drive (in this case it's C:\ for me) > Windows > System32 > Drivers > etc
Once there you will see a file called "hosts". The easiest way to modify this is to drag it to your Desktop
Once it's on your Desktop, open Notepad and drag the hosts file into Notepad. You should now see 2 lines under block comments (last line being: ::1 localhost)
After you that line simple add the IP address you wish to mask (your own or a server address etc).
Press TAB or simple just add a space after that; now you can put in whatever you want to be shown rather than the real IP address (don't use spaces, if you wish to use spaces simply use underscores; like_so).
Now, go to File > Save or simply press Ctrl + S
Drag the file back into the folder you dragged it out of (C:\Windows\System32\drivers\etc)
You're now done
It's as simple as that, now whenever you the IP is supposed to visible (take on a Minecraft multiplayer screen for example) it will show what you determined it to be in the hosts file, so my server on 127.0.0.1 would show up as YOU_WISH where the IP should be rather than the actual address.
I don't recommend doing this if you are unsure but it's what I personally do and I thought it would help those who are looking for an easy solution.
Hope this helps somebody out there; happy streaming.