Incarnations of Immortality, book 1: On a Pale Horse
Piers Anthony1983

When Zane shoots Death, he has to take the job, speeding over the world riding Mortis, his pale horse/limo, measuring souls for the exact balance of Good and Evil, sending each to Heaven or Hell instead of Purgatory. The new Thanatos is superbly competent, ends pain when he ends lives. But Satan is forging a trap for Luna, the woman Death loves.