Fake/Mock Sleep
Closing your eyes and pretending to sleep so the guy next to you won't talk to you.

Insominia
Closing your eyes and trying to sleep but you can't fall asleep.

Dozing Off
Closing your eyes and drifting in and out of sleep and you lost track of time of how long you have actually slept.

I think OP's case is dozing in and out which is normal for most people? I know a lot of people who like to take prescription sleeping pills and pass out for 8 hours+ on long international flights.