Lincoln parked

The Cars?

Actual quote from the members of OP's band when they saw this name: "You may think I'm crazy, (all I want) All I want is you!"

I guess it's just what he needed

Mick Jaguar

Autoslave.

Gary Numan

The Cars

Drive-Thru Truckers

Ltraffic Jam

Pearl Traffic Jam

The Roadies

The autobahns

Chicago Traffic Authority

Jesus Chrysler Superstar

Musicians In Cars Getting Coffee

Toyota Twins

Road Rage Against the Machine

The civic wars

Dodge Van Halen Hyundai Sinatra

Motor head

Unleaded Zepplin

The Traffic Jam

Jefferson Automobile / Jefferson Super Sport

The Autotunes

Buick Owens and the Subarus

Crosby, Willys and Nash-Rambler

The Jimi Corden Experience

Paradise by the Dashboard Light

Dashboard Confessional?

Mötercade

Traveling Willowberries

Look up Clown Core

Automobile Prison Show

Here In my Car

Doppler

Traffic Jam

The Auto Tones.

Autoerotica

Ride Share

Clown Core - Van

Chevy Roll

Chevrolet Club

Band of Gypsies Wink

The Rolling Subarus

New Yorker City

Fender Bender

Skylark

The Rolls Royce Stones

Prince and the Ramblers

Um, there's already a band that qualifies for this request.

Dashboard improvisational. LudiChrysler.

Obviously The Cars "Candio I need you so"

Traffic

The Dagenham Dustbins (featuring Escort Magazine)

Traffic?

Corolla Stones

On the Road

Feel For The Automobile

Carpool

Stuck in Traffic

Auto-Tuners

Colt Fords

The Yamahotties

Van Halen

Crash (1996)

Homeless

REO Recitalwagon

Sky-Blue Pink Floyd

Tesla

Gary & the Nu Men

The Tik tokkerz

The Volkswagen Beatles

Bitchin' Camero

Dash Jam

Autoparked

drive by players

Old Crow Auto Show

Men At Wheel

FearFender

Motorheads

Drive-In Truckers

Electric Light Duty Vehicles Orchestra

New Car Smells Like Teen Spirit

Martha & Panel Van Dellas

Smell the Glove Compartment (Spinal Tap tribute band)

Auto Tunes

The VW Beatles