From here:
So how 'bout it, boys and girls? What would YOU name the Homeland Security mut?
My suggestion: Snoopy.
Faltraz.
I’ve always wanted a dog named Faltraz, but I wound up naming mine Ernie.
Ahem, I mean mutt, of course.
I’d like to see the character reconceptualized as Warren Terrier.
Bushie, the Son of a Bitch! 
Pierre.
I’ve always liked “Natron” for a dog.
or what about:
-Fnord
-Bert (from the Bert the Turtle “Duck & Cover” films from the Cold War)
-Cujo
Duckin Rover.
Big Brother.
The same thing Steve Martin named his dog in The Jerk: Shithead.
Maybe we can name him after Tom Ridge, and call him The Dog Who Barks at Everything. 
Somehow I think the most ironic name for the Homeland Security Mascot would be:
LUCKY
Old Code Yeller
We have a winner!
I second the nomination for Old Code Yeller 
Why’d it have to be a dog? I like dogs. Some of my best friends are dogs. You, Homeland Security, are no dog.
Can we get a retroactive vote, and change the species? I vote WEASEL.
How about a snipe?
Cujo?
Warren Terrier is way cleverer than Old Code Yeller.
Joining McGruff the Crime Dog® will be Rex, The Treason Dog®.