We will never know for sure, but well researched and supported theories about who is behind the Q persona indicate that none of the people involved have ever seen the inside of a secure facility.

You could tell that Q Anon was fake from the very first post, because they said Q was the "highest clearance," a statement that is doubly incorrect. Q is an access, not a clearance. Confidential, Secret, and Top Secret are the only clearances—people with Q must have a Top Secret clearance. And, Q doesn't provide you access to higher level information about global politics than Top Secret, it provides you access to information about nuclear weapon design. None of the things Q Anon purported to have insight into were at all related to the actual information controlled by the Q access.

Remember that the best lies also have a kernel of truth in them. You don't need to have a Q clearance to say you have one on 4chan, 8chan, 8kun (etc). How would anyone validate your Q clearance? Instead you just post something plausible, but just out of the reach of validation.

I thought I had read that "Q" explicitly said that's where the name comes from

Or more plausibly, his day job is trolling imageboards.