You have 4 options if we're just discussing passing data. (If we're talking about just the username then you want Josh's response)
Passing parameters in the redirect (as Jack suggested)
return RedirectToAction("Index", "SuccessPage"), new {username = name };
Storing it in temp data (only works for 1 request)
TempData[Key] = name;
return RedirectToAction("Index", "SuccessPage");
Storing it in session (lasts as long as the session lasts)
Session[Key] = name;
return RedirectToAction("Index", "SuccessPage");
Storing it in the database and linking that data via their session id.
/* databasey code here */
return RedirectToAction("Index", "SuccessPage");
That's your full set of options from simplest to most complex. I'd suggest in your case you just pass the values in the URL (first one) as your system expands and grows you may want to consider trying out the other options.
It's worth noting that TempData doesn't last across a page refresh.