When one is trying to look thoughtful, one might pull one’s chin up a little, pushing out the upper lip over the lower and creating a pattern of depressions on the chin. Does this facial expression have a name, or a general term by which it can be referenced without describing it every time?
I always thought it was called a “HMMMMmmmmm…”, although that might be a colloquialism 
http://www.emotioneric.com/ See what he says.
I hate to be the incredibly serious one here, but…
Pensive?
Contemplative or Aloof, depends on the on-looker.
Pensive and contemplative describe the state the expression is supposed to convey, but I was looking more for a name for the expression itself (smile, grin, frown, pout, moue, etc.)