What is the name given to the phobia "fear of being embarrassed in front of people"?

The name given to the phobia 'fear of being embarrassed in front of people' is social phobia.

Social phobia, also known as social anxiety disorder, is a common phobia among anxious introverted people who can be considered shy. They may experience fear and anxiety when they have to partake in social activities because they don't want to embarrass themselves in front of everyone.