just replace the favicon.ico in root folder with your own

Here's a better approach.
All you have to do is name your icons "favicon_<sitename>.ico" and place them at the root of the kentico site.
Then replace the FavIconTag method as follows

app_code/cmspages/documentbase.cs: line 375
public string FavIconTag
{
get
{
if (mFavIconTag == null)
{
mFavIconTag = "";
string favIcon = "favicon" + CMSContext.CurrentSite.CodeNameColumn + ".ico";
if (File.Exists(HttpContext.Current.Server.MapPath("~/"+favIcon)))
mFavIconTag = "<link rel=\"shortcut icon\" href=\"" + ResolveUrl("~/"+favIcon) + "\" />";
else if (File.Exists(HttpContext.Current.Server.MapPath("~/favicon.ico")))
mFavIconTag = "<link rel=\"shortcut icon\" href=\"" + ResolveUrl("~/favicon.ico") + "\" />";
}

return mFavIconTag;
}
}