Somniphobia - the fear of sleep
The medical term of 'fear of sleep' is Somniphobia or Clinophobia. Some people who have this fear associate going to bed with dying. Symptoms typically include shortness of breath, rapid breathing, irregular heartbeat, sweating, nausea, and overall feelings of dread, although everyone experiences somniphobia in their own way and may have different symptoms.
For me, I can't sleep, but I want to, not fear of.
By the way, I am not aware of any example of celebrity somniphobes.