I am now the proud possessor of a stone gargoyle that sits on the step outside my house.
He has little horns, wings (folded) and sits with his chin on his hands staring out at the world.
I have been asking him all day, but he won’t tell me his name. It’s a bit rude the way he ignores me actually, but hey, he’s a gargoyle!
Any ideas what I can call him?
Mervin.
Pablo
Manny Calavera
Fjordinand
Constable Downspout
Congratulations on your gargoyle-parentage, or at least stewardship. Your gargoyle should be safe for the indefinite future. So far, the German-based “Gnome Liberation Front” has yet to embrace the cause of gargoyle-liberation in a Popular Front expansion of their original ideological commitment. 
Oh yes, the names. Ahem:
Screwtape. Wormwood. (C.S. Lewis would be proud.)
Uncle Fester.
Fester Bestertester. (a Don Martin/MAD mag. reference)
Imp-e. (tip 'o the hat to the bizarro TV evangelists, Jack & Drusilla Van Impe.)
Are you a football (U.S.) fan? “Sapp” is funny, but something of an in-joke… The Bucs’ Warren Sapp has been in a trash-talkin’ war with the Giants’ Michael Strahan over the validity of Strahan’s breaking Mark Gastineau’s single-season sack record last year; Sapp has been very vocal throughout his career of his intention to someday possess that record himself; unfortunately for him, though, he only managed to rack up six sacks last season. [I say this as a big fan of his: “Sapp, just shut up and execute. And good luck; I didn’t like that giveaway to Strahan, either.”] OTOH, Warren Sapp is at least a generous tipper in restaurants, at least according to one waitron who posted as much to a web site on the subject of celebrities’ tipping (not tippling) proclivities…
Adam (as in, short for “adamantine,” and appropriate for a first gargoyle. Tee hee, maybe you should get him a mate!)
Felix (ironically happy-sounding, and a bit of a play on “fixed”)
Absinthe. All gargoyles are really French, aren’t they?
Abby-Normal.
Grimace.
Michael Jackson (“MJ?”), Joan Rivers, Liz, Liza… (Just kidding! I’m sure your 'goyle doesn’t look anywhere as scary as those celebs!)
Goliath. Your gargoyle needs to be named Goliath. 
doubts that anyone will get the reference, but oh well
Is Iggy-Boy named David? are you referring to the cheesy made-for-network-TV sci-fi movie “Goliath Awaits,” starring Mark Harmon?
C’mon, give us the reference! (I showed you mine!)
I have three Gargies. Their names are George, Bernard and Shaw.
George and Bernard were my first two, both somewhat doglike with quite large wings.
Shaw is more human looking and sounds a little like yours.
I have no life. 
Oh, a name: Either Spud or Spike.
I think TheOnlySaneOne is referring to the cartoon show: Gargoyles.
Is this a boy-goyle or a girl-goyle?
Blix, Pox, or Blunder
Hugo, Victor, or Laverne
Mugwort, Nightshade, or Wormwood
Fred, Bill, or Jack
[nitpick]
I believe her name is Rexella, not Drusilla…not that there’s much of a difference.
[/nitpick]
Name? I like Thunk, for some reason. It has a good, solid sound to it.
Quasimodo.
That’s it, Dijon Warlock! Rexella! Gad, they were weird! Always mining the day’s news for evidence of the coming Armageddon…
<ho-hum>From the Disney Animated TV show Gargoyles. </ho-hum>
I vote for Angus, The Argyle Gargoyle That Gar-r-r-rgles Ger-r-r-shwin Gor-r-r-rgeously.
And try picking out the source for that, TheOnlySaneOne. 
I like Hugo. I also like Pablo, of course (20 minute response time… nice!).
I believe the Goliath suggestion is from the Gargoyles cartoon of years past.
What do you mean"were weird" Scrivener? They’re still on TV where I live. Jack’s still blathering on about the EU and the Mark Of The Beast references in newspaper articles and how great it is that Jesus is coming back soon. After telling us about all the horrible stuff that will happen first. Rexella’s still holding up “cute” editorial comics. She’s so flighty, they must bolt her feet to the floor just before taping.
Gargoyle name: Mom
How about Brooklyn, Bronx, Hudson or Broadway? Or Demona if it looks female??
Howzaboot…Bitey