Naming controls within a usercontrol

I'm trying to create a usercontrol that contains several controls within it.  A TextBox, a label, and a couple of buttons.  This usercontrol will then be used in an aspx page.  However there will be more than one instance of that usercontrol within the aspx page.  The problem is that the controls within the usercontrol get repeated in the aspx page and because they are named the same of course things don't work.
I can think of two things that could possibly solve this problem: somehow name the controls within the user control based on the usercontrol's id, or encompass the user control within something that hides the controls from being exposed; some sort of template.
Thanks for suggestions.