By Chris Gallant AAA |. A: An underage person cannot open a brokerage account on his or her own. However, it is possible for an underage person to have a brokerage account with his or her own name attached to it, but in order for this to happen, a parent or guardian must also be involved with the account.There are a few different ways this can happen.owever, it is possible for an underage person to have a brokerage account with his or her own name attached to it, but in order for this to happen, a parent or guardian must also be involved with the account. There are a few different ways this can happen.