BNY Mellon Disbursement does not appear on Turbo Tax for my 1099 R entry. Should I use just the BNY that comes up on turbotax

If it does not match the name on the form, you should not use it. Start by checking if your financial institution or brokerage is a TurboTax 1099 partner (scroll down and select the 1099/1098 Partners tab). If your institution isn't on the list, you won't be able to import.  BNY MELLON | PERSHING is on the list.  If that matches your Form 1099.
 

If it is not listed, you can enter your Form 1099_R manually as follows:

You can do the following in TurboTax to delete or enter a Form 1099-R:

1. Continue your tax return
2. Click on the Search icon at the upper right of your TurboTax screen
3. Type "1099-R" in the search bar and hit enter
4. Click on the link "Jump to 1099-R"
5. This will take you to the 1099-R section of your TurboTax program.
6. if you need to add a Form 1099-R, select "Add another 1099-R"
7. You can select "I'll type it myself" to enter it manually.
8. To delete the form, you can click on the garbage can next to it

Click here for instructions on where to enter your Form 1099-R.

Click here for "How Do I View and Delete Forms in TurboTax Online"

Click here for "How to Delete Forms in TurboTax Desktop".