Pen names

Why did writers use pen names instead of their real names? I have often wondered about that. Some used pen names because writers were not considered to be serious people or serious about their other profession, be it lawyer or statesman or whatever. Then some wished to avoid the notoriety of having their names known to the public. Now the reverse is true and most seem to seek the limelight and the attention that goes with it.

Pen names:

George Orwell, real name Eric Blair

Anthony Burgess, real name John Anthony Burgess Wilson