"Nocturnal seizures" is the word you're looking for. Contrary to what you may think, your brain is not actually at rest while you sleep. Just different parts are active! I have nocturnal epilepsy....was "lucky" that my first episode was status epilepticus, or multiple grand mal seizures in series that I did not wake up from. My dh woke up, called the ambulance, and I seized in front of witnesses all the way into the ER. So even though seizures (or even instability) were never detected via VEEG or sleep-deprived EEGs later on, my diagnosis was never in doubt. After that first episode, I had two or three more nights of repeated grand mal seizures that my dh was able to wake me up from (while on depakote; apparently reduced the severity but not frequency). Then on keppra (plus now lyrica), they're mostly under control. Oh, but what I meant to add, sorry got sidetracked in history, is that yes, I would wake up with a horrific headache and exhausted.
I say I'm "lucky" because I would have HATED it if the doc, upon looking at my normal test results, would've told me I was imagining it or whatever. I can only imagine how frustrating it must be to have things going on during sleep and not have it documented!
Mine are mostly "catamenial", meaning they came before my period, hypothetically during the decrease in progesterone before the decrease in estrogen. I think that's the main reason, fwiw, that my test results came back negative. At the time that I scheduled the testing, they only could "fit me in", they couldn't schedule at the most likely time for my head. During the rest of the month, my head is quite stable, so the results were not surprising to me. (unlike last night, but that's another post)