This is called "income in respect of a decedent" and is discussed here.
https://www.irs.gov/publications/p559
As long as you are the person who is the beneficiary or the person who has the right to this income after the other person's death, you report it on your tax return as if it was in your name.
(You could contact the payer and ask them to cancel the 1099-DIV and reissue it in your name, but that's not really necessary. Just keep good records.)
