The medical term for sleep drunkenness is confusional arousal. Confusional arousals belong to the group of non-REM-related parasomnias. It's the inability to wake up fully and be oriented to time and place. This confusion lasts for a few minutes in most cases. It's more common when you wake up from deep sleep, especially in the first half of the night. However, it can also occur when waking up in the morning.
