No, you do not need to issue 1099s between your deceased father and his estate.
It is a common situation for an estate to receive a tax reporting document issued under the decedent's name and ssn if the payer of the 1099 did not have the name and federal ID # of the estate to issue it correctly. You could contact them to see if they will reissue under the estate name and EIN, but it may not be something they will want to do anyway,
If IRS has questions, they may send you and/or the estate a letter of inquiry, which you will need to respond to and explain what happened so they can follow it.
