Pretty sure the IRS doesn't really care because they would be able to match up your account number from your return with the 1099 Fidelity filed with them. However, my Fidelity Investments 1099 has the Payor's Name and Address field as: National Financial Services LLC.
Pro tip: the easiest way to handle this is to import your 1099 directly from the Fidelity website. Saves you time and avoids mistakes.