For a 1099-B it doesn't matter what you enter for the name of the bank or brokerage. It doesn't go on your tax return. It's just used in TurboTax to keep track of the various financial institutions. So use whichever is more meaningful to you - probably the company. What actually goes on your tax return is the description of the investment that you sold.
Somewhere on the page it should say "Payer's name." That's the name of the company that actually issued the 1099-B. It might be further down the page, possibly on the right.