In Persona 1, Thanatos is Yuriko Yamamoto's Persona and is the boss of eponymous Thanatos Tower. In Persona 3, Thanatos is the ultimate Persona of the Death Arcana instead and is associated with Ryoji Mochizuki.
Thanatos is my favorite Greek god (honestly don't know why). He doesn't show up much in mythology, but two major episodes are 1) his battle with Herakles and 2) his battle of the wits with Sisyphus.
The book referenced above is "On A Pale Horse", by Piers Anthony, the first of his Incarnations of Immortality series. Thanatos is indeed the Incarnation of Death, providing the necessary service of assisting the soul's departure from the body at the end of one's life. Thanatos' function also requires him to determine the soul's destination; heaven, hell, or purgatory. I cannot remember if any back story is included regarding the origin of Thanatos' name, but his horse is named Mortis, the Latin word for "death". Appropriately, his appearance is that of a hooded and cloaked grim reaper, skull-faced and all.
In Persona 3, Thanatos is the ultimate Persona of the Death Arcana instead and is associated with Ryoji Mochizuki.