There's no phobia word for it (I don't think), but I have the fear of Eternal Oblivion - a.k.a. Nothingness after death
Though I'm still living, I have a deep fear of death and what happens after. I like to think of myself as a slightly religious person, but knowing there's no real 100% proof that we go anywhere after we die frightens me. I fear dying and that being it. The thought of all the lost souls who died before being completely obliterated haunts me and thinking I could end up the same way keeps me up at night sometimes. Worrying if my soul will just become as non-important as the stars that vanish without a trace someday...It's terrifying...