My first idea was “Don’t Drive Like My Brother!” which was already suggested, so my second choice would be a spin on the old This Old House series and be “This Bogus Garage!”
Alternator Universe----Just the place for us all to be-----
Car Walk (seeing as we’ll be seeing them)…and have a lil PBS’y thing showing a number of cars walking, i.e., a lil pink car walking daintily while appearing to hold up its skirt, a big monster SUV strutting its stuff down the street, a low-rider car scanting down the boulevard holding up its pants (from falling down!), and then Tom and Ray – along the lines of “which of these doesn’t belong?” Keep the name as close to NPR show name so the fans can find it, and so you don’t bring in too many of the “unwashed” for the first episodes. Once the press gets wind, they’ll bring in the unwashed! This isn’t “The Simpsons at 60” or “Family Man goes to MIT” this is our Car Talk fellows…in a better form than they are now! 
Call it “Car Talk”. Why would you call it anything else, other than a misplaced sense that you’ve got to come up with something new?
How about simply “The Mechaniacs”. After listening every Saturday morning for over 10 years, I think it fits perfectly.
“Car-A-Bunga”, “On-Air Car Lacheys”, “All Car Things Considered”, “Stump The Chumps”
How about…“Unencumbered by the Thought Process”?
NUTS AND BOLTS;
(Them that aint nuts, have already bolted!!
“Our Fair City”. Tom uses the the phrase every week and it kind of encapsulates the look of the cartoon.
Grease Monkeys
DON’T DRIVE LIKE MY BROTHER
How about Stumping the Chumps or The Stumping of the Chumps - or maybe just Chumps? 
You Auto Laff–Like Us
I like “Rear Ended” or
I’ve seen “Dip Sticks”, but my improvement is “Dip Schticks”.
can’t wait to see the show!
Suggestions:
“The Backfire Brothers Car Show”
OR
“Clunk and Junk Car Show”
OR
“The Bender and Fender Car Show”
Don’t Drive Like My Brother
Click,Clack…Car Talk!
Our Lousy Show
The Lousy Car Talk Show
Click and Clack’s Lousy Show
“Our Fair City” or
“Hello, You’re on CarTalk” or
“Stump the Chumps” or
“Don’t Drive LIke My Brother”
How about “Tuned Out” – As in carTOON, tuned car (or untuned), tuned out (which is what what can happen when a caller asks Tom and Ray questions), questions and answers that are out there; this list can go on… – Amy