The downloaded TurboTax software can only be used with one TurboTax account. The software is tied to the account that it's purchased under. You can file your son's tax return under your account. He does not need a separate account. As far as processing of the tax return is concerned, it doesn't matter what account it's filed from.
If you feel a need for separate TurboTax accounts for some reason, you would have to buy two copies of the software (one in each account) and install them on separate computers.
