Can we pair one remote with Mac, and one remote with AppleTV in the same room? I got AppleTV and it came with a remote.  Since the remote triggers action on both the AppleTV and iMac (they are in the same room), I disable the iMac from taking remote signal already.

But can I buy another Apple remote, and pair it with the Mac, so that this new remote will not trigger action on the AppleTV?  That is, one remote for the Mac, one remote for AppleTV, and they don't interfere with each other.



Update: I actually went down to Apple Store and got another remote, and paired it with the iMac, and confirm that this remote will not trigger any action on the Apple TV, so now each remote works independently... I just put a sticker on one of the remotes to tell which is which.
Yes. Follow the instructions in this Apple Support article for Macs or this other article for Apple TV.

Essentially, the procedure is this:


  Pairing your remote with your Mac:
  
  
  Log in on your Mac as an Admin user.
  Get very close to your Mac (about 3 or 4 inches away).
  Point the remote at the infrared sensor on the front of your Mac.
  Press and hold the Menu and Next/Fast-forward buttons simultaneously on the remote for 5 seconds.
  Your Apple Remote is now paired with your computer. You should see a chain-link style lock appear in the center of your screen for a moment.
  





  To pair your Apple TV with a remote:
  
  
  Choose Settings > General > Remotes from the main Apple TV menu.
  Choose Pair Apple Remote.