Is it bad to use user name as primary key in database design?

I was told by a friend:

What unique key do you use? I hope you are not saving the entire user name --- this will use up too much table space! Assign an unique userID to each (unique) userNAME and save this userID (should be INTEGER UNSIGNED auto_increment or BIGINT UNSIGNED auto_increment). Don't forget to create a reference

FOREIGN KEY (userID) REFERENCES usertable (userID) in all tables using the userID.

Is the above statement correct? Why or why not?