Why is the band name PSY?

Yes, his stage name 'PSY' is short for PSYcho (which is the name of his fanclub/fans). :)

The name Psy was a mix of his real name and for his first album 'Psy From The Psycho World' and he is not part of a band, Psy is a solo Kpop entertainer and he has back up dancers for his performances, they do not sing with him.