Trouble renaming IIS Website.

I have a web server. IIS on Windows Server 2008 R2. It'a a production server which runs many applications for my company.



Every time I open the IIS Manager I can see that "Defaults" as the name of my website. It really itch my eyes for month. But today I decided to change the name to something else.I think about name it the same as the domain name. So I try right-clicking the "Defaults". Owh, there's a "rename". Maybe I should try it.