In short, it's required. Securities regulatory authorities and the IRS require that all brokerage firms record the full legal name of account holders. An account cannot be opened without this information. In addition, errors in this field may prevent your account from being approved for trading, so don't enter your nickname or alter-ego.
If you are opening a joint, custodial, or ESA account, you will also need to enter the full legal name of the secondary owner, child or beneficiary (respectively) of the account.