What's the psychological issue name of fear of people? With the issue of being afraid of doing anything before people, one has to work hard on self control to prevent the body shaking on every tiny action, like hold a pen, drink water, etc, and when there's many people looking at him/her, it becomes almost impossible to hold shaking, to speak normally, or to think. This person is subconsciously in fear of people unhappy(?) with his actions, even though he knows there's nothing wrong with his behavior.

Is this a typical case in Psychology? Is there a name for it?

Scenario for some background information his mother died when he was very young, his father don't like him, never talked to him except call everyone dinner, never smiled to him, never spent time with him, never gave any recognition even he got full marks, curse and beat him on whatever excuse when not in good mood. 

He lived in a room with a big window in the wall next to the living room(a request for curtain was rejected), he had no idea why father dissatisfied with him (he's always one of the best in his class during student period and never asked for anything from his father, if exclude care), but been used to keep an ear out on his father all the time when at home, for whenever his father step into the living room where he would be seen through the window, he could sit as straight as he can before his desk and try not to move a bit, he didn't want to give him any excuse to curse, to beat.
The general symptoms (NOT the background scenario) may point to a psychological disorter called  social phobia :

Social anxiety disorder (SAD), also known as social phobia, is an
anxiety disorder characterized by a significant amount of fear in one
or more social situations, causing considerable distress and impaired
ability to function in at least some parts of daily life.
...
Physical symptoms often include excessive blushing, excess sweating, trembling, palpitations, and nausea. Stammering may be present, along with rapid speech.
...
The first line treatment for social anxiety disorder is cognitive
behavioral therapy (CBT) ... . The cognitive and behavioral components
seek  to change thought patterns and physical reactions to
anxiety-inducing
situations. ... . Prescribed medications include several
classes of antidepressants: selective serotonin reuptake inhibitors
(SSRIs), serotonin-norepinephrine reuptake inhibitors (SNRIs), and
monoamine oxidase inhibitors (MAOIs)
...
It is the most common anxiety disorder with up to 10% of people being affected at some point in their life