I don't think you can transfer what you already bought, but you can open a custodial accounts for them and start buying. Good deal from here still. Good luck !
If you need to keep the shares in a custodian account (say you are giving shares to your grandson or granddaughter who is a minor to keep in a college fund, your son in law or son/daughter can act as the custodian), you will need the custodian's bank info. Once you have filled out the forms that your broker sends you and the custodian has opened a custodian trust account at his/her bank, your broker can then transfer shares directly into the custodian trust account in the frequency and amount of your choosing.