But when the minor child is not yet ready to assume responsiblity for his or her finances it would be better for an adult to be appointed to manage the minor child's finances.
Otherwise, if the amount of money is significant the minor child's guardian will likely have to open a court proceeding and petition the court to be appointed guardian of the money. A court proceeding would likely be expensive and, at very least, delay distibution of the money.
Financial Custodian and the Uniform Transfers to Minors Act (UTMA)
Almost every state has adopted the UTMA which governs the distribution of funds to minors. The UTMA makes naming a P.O.D. Payee custodian simple. To name a custodian as the P.O.D. payee and require the custodian to hold the funds for the minor child simply write on the form provided to you by the bank "[Custodian's name], as custodian for [minor child] under the [state] Uniform Transfers to Minors Act."
If the minor has not reached the age for termination of the custodianship when the bank account owner dies, the custodian will hold the money until the minor child reaches the age for termination of the custodianship. In most states, the custodianship will automatically terminate at the age of 21.
For more information on pay on death accounts read my article Payable on Death Bank Accounts.