No, you do not need to issue a Form 1098 as an individual holding a mortgage.
However, you do need to give the buyer a statement showing the total mortgage interest you received from them, your name, address, and Social Security number. With that information, they will be able to claim the interest paid on their return and you will show the interest as income on your return.
FYI ... you will also need their name, address & SS# for your return to report the interest income on the Sch B.
If you received interest income you will enter it with these steps: