Change site name programmatically

I am using this code to change site name, but with no success:

SPSecurity.RunWithElevatedPrivileges(delegate()

{

     using(SPWeb oWebsite = SPContext.Current.Site.OpenWeb("Website_URL"))

{

   oWebSite.AllowUnsafeUpdates = true;

   oWebsite.Title = "New Website Name";

   oWebsite.Update();

   oWebSite.AllowUnsafeUpdates = false;

}

});

The code executes with no errors, but the site name is still the same. What am I doing wrong?