Is there any actual name for the fear of dying?

Thanatophobia. An unusual, intense fear of death or dying is called thanatophobia. A typical amount of fear would be normal and not called a phobia. Treatment of phobias is available for people who have trouble living normal lives due to their phobias.
Necrophobia. There are actually two terms: thanatophobia -- fear of death, while necrophobia is really the fear of dead things or anything associated with death and dying, including coffins, etc.