 There is an adjective, semisomnus, which means half asleep. And there's a medical term, hypnopompic, which describes that semi-wakefulness period between sleep and full consciousness. But that's still not, it's an adjective and it's still not describing the time period. It's still describing you, your own mental state. And then there's Japanese, utouto or utsura, which is about fluctuating between being awake and being asleep.