Mosesi & Kalantarian, LLP

Yes, you must list all of your debts on your bankruptcy schedules, even debts that are non-dischargeable or secured.  
However, you can choose to reaffirm any debt you choose after the filing.  Or, you can voluntarily pay a creditor after you receive a discharge, without becoming legally liable to continue paying.
Thus listing a creditor does not prevent you from paying creditors you wish to pay after bankruptcy.
Also, omitting a credit card company from your schedules, because you want to retain the use of the card, does not assure continued access to the card:  most major credit card issuers use a national data base to determine who has filed bankruptcy, independently of the court's notice to them of bankruptcy filings. They routinely cancel cards of everyone who has filed bankruptcy, whether or not a balance is owed.
You can't assure that your creditors won't find out about your bankruptcy by not listing a debt.  And omitting a debt constitutes perjury which could result in your discharge being denied.