Most folks associate “BYO” with “Bring Your Own (beer)”; the magazine by the same name is “Brew Your Own (beer)”.
It’s not terribly clever, but the name Modern Drunkard always makes me laugh a little inside.
I came in to say 2600 because I figured there was no way in the world anyone else remembers that was a thing but I should have known better 
I like Fangoria, the magazine for fans of horror films. Very cool that they get “fan,” “gore,” and “fang” into the same word.
Infocom, the company that used to make text adventure games, had a quarterly newsletter called The New Zork Times. (“All the Grues That Fit, We Print”). Until the Gray Lady told them to knock it off and they re-titled as, I think, The Status Line.
Wow I forgot about that nifty little periodical.
My mom also used to subscribe to a newsletter called The Underground Grammarian and a quarterly called The Utne Reader
I could list a bunch of scungey punk/hc/metal zine titles from back in the day, heh, if I could remember any.
Of course, what list of clever magazine names would be complete without mention of Rita and Uncle Trevor’s Bumpaddle Magazine.
Surprised no alt-righters have come up with a MAGAzine.
Crawdaddy
Oh, and Girls and Corpses Magazine.
The cleverest magazine title of all time belonged to sadly defunct New Zealand feminist magazine Broadsheet.
Unusual, although you might not call it “clever,” was a magazine that published just a handful of issues (4?) in the 1960’s, Horseshit, put out by the two Dunker brothers in Hermosa Beach, California. Subscribe and you got a handful of posters as a bonus, with text like, “Buy Bonds, Burn a Baby,” and “Be a Man,” illustrated with a soldier in full battle dress, his pants down, sporting a rather diminutive penis.
Needless to say, the army didn’t like those posters much when I put them on my locker. The army is not a good place to try to assert free speech.
Apparently the asserting part went just fine; it might be the defending that’s the tricky part. 
Two weeks late but if you’ve a deep interest in phreaker history, I recommend Exploding the Phone, which covers from the earliest days* on up to when everything fell apart. Even before the famous Cap’n Crunch whistle there was the Dan’l Boone Bird-calling whistle which you could buy at a five and dime store.
Full disclosure: I know the guy.
*Hell, he even covers the rise of the Bell System and the engineering triumph of fully automated long distance direct dial, which is what set things into motion.
Actually, I would have thought it would have been a magazine for certain muscle cars of the 1970s.
Mythopoeia which was about created fantasy universes and mythologies, especially Tolkien’s.
Heeb magazine (subtitled “The New Jew Review”). The magazine ended in 2010, but they still have a website.
The there is the horror magazine that’s only published on braille. It’s called ‘Feel and Scream’.
Ok, I’ll go now.
No, please stay! That was funny!
Prof. Pepperwinkle, are you sure there was a magazine named Mythopoeia? I can’t find any mention of it. There’s the Mythopoeic Society, which publishes magazines like Mythprint and Mythlore, as I mentioned.
There’s a medical journal dedicated to cerebral infarctions called Stroke. I’m reluctant to try to find the link to their site as I don’t really want to Google “stroke magazine” at work.
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