Frenchie (think on that for a second…)
Artemus, original or remake version.
Just depends on if you want the little fella to feel kinda vintage or uber hip. 
“Harmless”. What? You never heard that “a little aardvark never hurt anyone”? 
There’s only one proper name for any pet aardvark.
Cerebus, of course.
[sub]It’s not that nobody will get it…it’s that the RIGHT people will get it.[/sub]
Oh yeah, you win!
Not only did I get it, but I am profoundly aggravated that I did not think of it myself.
DeathSnout, Aawesome, LardLark, Revalache, BigMoney, Antspants, Tak, Whale, Blargh, Shaolin Monkey, Anabella, Julie, Yarrmaggedon, Tastybugs, Redallover, 4 legged freak.
That’s all.
Oh, wait! I almost forgot.
Choose Cerebus, of course! 
How 'bout “Aardy Arr Arr”?
It’s a lovely name, that one.
Well, so far, Cerebus is in the lead for the Most Obscure. But, we’re not looking to trample anyone’s copyrights, here.
Contenders for the top prize;
Nelson Aardvark Mandela
Artemus (always liked the name, and I liked the original character, too)
Aawesome
Bob
Harv (I don’t work for Al’s Aardvarks and Auto Alignments, nor do any of my relatives. At least, not the ones I acknowledge.)
Leading the pack for Most Humorous;
Jo
Don’t give up folks. The rules, as Aslan, tanookie, and Wyatt so astutely noted, do not limit a contestant to a single entry.
Oh, and we do call him and “odd-vahk”. You just can’t hear us.
Personally, I like Aarty and it certainly could be the diminutive of Aartemus.
Aartemus (Aarty) Aardvark III has a certain je ne sais quois. Friendly, yet learned.
I’d also like to nominate OddVahk as the best smartassy answer yet! Good Job, X~Slayer!
Aahnold. No, Aargyle
Or Kravdraa.
Wait- this it it: Ah’m a’gettin’ Aardvark!
Aaron, does he look Jewish?
aarsehole the aardvark
kravdra
Surely the aardvark (don’t call me Shirly)
Aare Aardvark
Adrian Aardvark
Aelfric Aardvark
Alva Aardvark
Arp Aardvark
Aurelius Aardvark
Clark Aardvark
And finally:
Fred the Aardvark
Name him Oldsmobile.
Oh, and I might be wrong on this, Dave, but the original Arthur the aardvark did have a nose…not on the cartoon, but on the cover of one of the first Arthur books. It was…well, it was disturbing. I’d guess the nose was phased out because it frightened children. But I agree: they should have given him something. He should have a suitable aardvark nose, or else he should not be an aardvark.
And may I just say that you guys have selected one of the top ten coolest animals to have as a mascot. Aardvark is right up there with wombats and yaks. Excellent choice.
Name it Frunobulax.
Or name it Managua
Call him “Fonzie”. 'Cause everything he ever said started with an “A!”
Now I’m reaching.
So far, the only one that really jumps out at me is Harv. “Pahk the cah neah Hahv Aahdvahk,” wish I’d thought of it, in fact.
But Bob would be good if we could work it into conversation. You know, “just follow this street to the third stop sign, hang a left and Bob’s your aardvark,” something like that.
Dr. Ardvarkian?
Sorry, but while I know who Cerebus is, I’m not getting the reference. Will someone please explain it to me?
Apologies for my idiocy.
Neither did I, but googling for '“cerebus aardvark” found a reference to an aardvark called Cerebus, which I assume is the reference.
I keep reading ‘Cerberus’ instead of ‘Cerebus.’ It’s confusing.