As long as other computers, or routers, on the network want to send you information yia TCP/IP they need to know your IP address. If you don't want any communication then just pull out the network cable.
Why would you want to hide your IP address on the local network?
In my organization there is a Think Room that we can post our opinion on it But there is a problem , by the time we send an opinion that is not polite or by any other reson the manager can see who posted the opinion by its IP , and I decide to post an opinion that they can't recognise me. thanks
If the consequences of your being found out are bad, then don't do it. Find some other way to express your views. Suppose that you could fake your IP address and use someone else's; then you would get them into trouble.
Unless you are very clever, and have control of the network, never rely upon anything that you do on it as being private. It is very easy for a knowledgable person to monitor communications.
I don't use Facebook (because I too value my privacy).
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