I can also tell you that, if you swap out "booze" for "benzo" in the OP, it would just be called a hangover.
What I mean is, if you drank a fair bit, passed out/fell asleep, and then woke up abruptly, it would be a bit expected, as a mild withdrawal. It's why you're advised not to drink before bed, since you'll probably just wake up in a few hours and really be an insomniac.
Benzos work the same way. If you have a benzo habit and wake up most mornings with anxiety? Yeah, that's how it is with alcoholics--withdrawal. Maybe milder, maybe there's a better word for it, either way it's the rebound anxiety that must come as your GABA levels readjust and your NMDA receptors spark.
Otherwise no, it's not normal to wake up anxious, fast or slow (I mean, unless it's some explosion destroying your bedroom, that'd be anxiety-producing).