Carefully choose your false name. Some people prefer to use an initial instead of a first name to prevent readers from knowing if the author is male or female.
Do some research on the false name that you have chosen to make sure that there is not already another author with this name. Also check to see that there are not already famous characters with the same name that you have chosen.
Contact an intellectual property lawyer for advice if using your real name to collect royalty payments would be a danger or risk.
Notify your publisher of the false name that you wish to use, so that it can be the only name associated with your publication.