It's called a Size Grip
https://msdn.microsoft.com/en-us/library/windows/desktop/dd373644%28v=vs.85%29.aspx

Visual Studio seems to have the option of "Auto" as well as "Show" and "Hide" in form properties. I dont' know where Auto would take its setting from but my fairly clean (in terms of GUI) install of Windows 7, Auto=Hide.