Why is my computer name new-host-2.home on the network? I configured my computer name to "Macbook of Matthieu" in the network sharing preferences.

However, this name end up being used: new-host-2.home, how can I change that?
The ".home" domain sounds like it might be something your router is providing. Check your router's settings for a DNS server configuration. If you want to use the Bonjour/mDNS ".local" names, then turn off the router's DNS server, or tell it to act only as a proxy for your ISP's DNS service.

Unfortunately, the specifics of these settings, and even how they are named, vary widely across routers. You will have to look up instructions for your specific router model.