If one person's SS# is on the tax forms then the IRS will expect ALL of the income to be reported on their return which can cause headaches in the future with the IRS since you can nominee interest and dividends but not stock sales. The correct reporting will take time and effort so it would be wise to get the account split between the 2 of you by the broker so you each get your own tax reporting form and avoid IRS audit letters in the future.
