Question

What term refers to having a high concern with others perceptions of us and adjusting our behaviors to the situation?

Answer 1

I believe the answer is: Power

In the past, this power is mostly derived from nobility line, but In our current society, Power usually derived primarily from economic power. 
For example, someone in company's Upper management position tend to always required to maintain their persona in order to keep a certain amount of respect/positive perception from both the workers and the public.