The answer is:
If you think hard you can earn my name.
A college/university degree
All that thinking might raise my power over you.
Powers (mathematical) use the term degree: 4 to the 12th degree is 4 to the power of 12
Dont worry, I can prevent that from showing.
Degree is a brand name for antiperspirant/deodorant in the US
I am alone... Yet there are many of me.
Relationships are measured in degrees (think Six Degrees of Kevin Bacon).
It burns you, not knowing my name.
Heat is measured in degrees
Does it make you want to kill?
First degree murder, e.g.
How far are you willing to take this game?
Movement/motion is measured in degrees like "three degrees of freedom"