Am I required to correct my opponent's assumptions about my morph creatures?
You are required to say which card was the Deathmist Raptor when asked, and you are required to correct their mistake if they get it wrong.

The Magic Tournament Rules define free information as follows:


  Free information is information to which all players are entitled access without contamination or omissions made
  by their opponents. If a player is ever unable or unwilling to provide free information to an opponent that has
  requested it, they should call a judge and explain the situation. Free information consists of:
  
  
  Details of current game actions and past game actions that still affect the game state.
  The name of any visible object.
  The number and type of any counter that isn’t defined as status information.
  The state (whether it’s tapped, attached to another permanent, face down, etc.) and current zone of
  any object or player.
  The game score of the current match.
  The current step and/or phase and which player(s) are active
  


Putting the Deathmist Raptor onto the battlefield face down was a past game action that still affects the game state. The details of that action include the name of the card that was moved from the graveyard (which was free information at the time), and which face down permanent that card became (because you need to distinguish which face-down permanent is which as mentioned in the question). You must provide that information when asked, and you must correct them if they get it wrong so that you are not hiding the information by omission.

Strictly speaking, the current identity of the face down Deathmist Raptor probably counts as private information, because that information is not explicitly listed as free or derived information:


  Private information is information to which players have access only if they are able to determine it from the
  current visual game state or their own record of previous game actions.
  
  
  Any information that is not status, free or derived is automatically private information
  


There is no rule against misrepresenting private information, but the distinction between "This permanent is currently a face-down Deathmist Raptor" (private) and "This permanent was previously a visible Deathmist Raptor card that was put onto the battlefield face down" (free) is so small that I suspect that most judges would not look kindly on using it as a reason to misrepresent or omit that information.