Wikipedia has more on Monophobia
Monophobia (or autophobia, uniphobia, isolophobia, eremophobia) is the fear of being alone. Sufferers may fear in every place, like in home, public places, or out in the nature. At homes, sufferers may worry that someone may break into the house or of getting injured without help. Fear of being alone in public places is often linked to sociophobia and agoraphobia. Sufferers of public places may fear getting robbed or of somebody attacking them.
Sufferers would panic when the loved ones leave the home, either when going out to work, eat out, visit friends, or participating in a hobby. More severe monophobic sufferers may be afraid for the loved one to be in a different room of the house.
The fear can be coped by communicating with people via phone or email. When not communicating, they may want to hear background noises, like from outdoors, and do things like watch TV, read books or newspapers, go on computer, or listen to music. When going to public places, they may need to bring tablet, smart phone, mp3 player, etc.
- Monophobia - the Fear of Being Alone about.com