Not only consciously named after an aeroplane but also designed in its manner, the GM LeSabre:

Often mislabelled as Buick but they pinched the name later.

Rambler Nash-Kelvinator Ambassador American Motors Jeep Chrysler Fiat Mercedes Benz
 

Not in the "brand engineering" sense more common recently. As w/ General Motors, which happened earlier, there was consolidation in the auto industry post-WWII. My 1949 Nash, and a shallow refrigerator w/ all glass shelves and no detail on the inside of a plain sheet door except a War Board price label, were made by the Nash-Kelvinator Company. At least the Nash part went to Rambler, which went to American Motors (which also got Jeep, which was why Chrysler wanted it), which (Jeep) went to Chrysler, which went to Mercedes Benz for a brief period before merging with Fiat...and now some further changes in the works I think I read somewhere.
Technically, there seems like a certain innovative trend in engineering that carried through from Nash through Chrysler. (Nash had early uni-body, front seats that folded to make the whole interior a large bed, a piece of exhaust tubing for an exhaust manifold and no arches in the front fenders for turning of the front wheels...which required a narrow track, created an odd appearance, and probably killed the brand. Chrysler had torsion bar suspension for awhile, which may have come from Packard or someone else they absorbed?)

From what I understand, Rambler was a Nash model, which then became a brand in its own right when AMC was formed.

That got me to thinking about the AMC Pacer, like an upside down goldfish bowl. Very odd on UK roads with a gigantic offside door and a smaller one by the kerb. There's one still around here or was until very recently.

I'd only ever heard of the Tri-Pacer, which looked futuristic to a very small boy in the 50s compared to the usual fare of Tiger Moths and Austers, and thought from the name there must have been a Pacer.

There was...
Piper Pacer, AMC Pacer.

all this AMC stuff sparks memory: Gremlin was their Hornet with no trunk. What were the little planes that launched out of a large WWII(?) era mothership?

At least one Nash Rambler model had front-seats that folded back to make a double bed:
Nash Airliner Reclining Seats | Modern Mechanix

There are stories of fathers refusing to allow their daughters to go out with boys who had a Rambler!

Goblins, from B-29s & B-36s

Goleta Air and Space Museum: Flying Aircraft Carriers of the USAF: McDonnell XF-85 Goblin

There are stories of fathers refusing to allow their daughters to go out with boys who had a Rambler!

That would be the fathers who, as a boy, had a rambler themselves, then.

Morris Oxford

Not BL Avenger - Hillman and then Chrysler.
I had one briefly and hated it with a passion.

Standard Envoy, Airspeed Envoy. Not really fair the car was first by a couple of years.

Aston Martin Valkyrie - North American Valkyrie.

A couple now where the aircraft production exceeded the cars.

Aston Martin Bulldog - Bristol Bulldog.

Bugatti Atlantic - Breguet Atlantic.

Armstrong Siddeley Hurricane
 

Not the best example but it only cost £30

Fantasy Air Allegro - Austin All Agro (aka Allegro)

There was also the Campbell Cricket gyroplane, and the Morane Saulnier built Fieseler Storchs were known as Criquets!

A real oddity was an American automobile produced about 1946/47 (a typical saloon car of the era) which was called the "Bomber", and very specifically attributed to its unusually styled "nose" (an ugly protrusion from the radiator grill) which was supposedly inspired by the very distinctive nose of the B-29. Why oh why would anyone want to do that ? - it was a CAR!!! Apparently (and in my opinion rightly) it was never considered an American classic. Unfortunately I cannot recall the manufacturer, but somebody on this thread will know it, could have been a Ford, or Studebaker maybe.
David D

Indeed - I had one for 12 years - but there was also a Reliant Sabre.

Speaking of Reliants...

Dart Kitten - Reliant Kitten

There never was an American produced sedan/saloon car called the "Bomber". You are probably imagining the Raymond Loewy designed (and executed by Virgil Exner) 1950-51 Studebaker "Bullet Nose" Commander. Why? Automobile design has been inspired by aviation for decades, and has incorporated many aeronautical design cues.

https://i.imgur.com/FFspoRz.jpgDesigned to emulate a jet engine intake. The 1949 Ford also had a circular intake grill design.
https://i.imgur.com/i9UzVqX.jpg


Chrysler produced another Avenger. The Dodge Avenger is a front-wheel drive, mid-sized sedan that was built by Dodge. The Dodge Avenger made its North American debut in 1994 as a two-door coupe, which was produced until 2000. It was re-introduced to the market as a four-door sports sedan starting in 2008. 2014 marked the last production year for the Avenger, as models for both the Dodge and Chrysler brands were consolidated into the single 2015 Chrysler 200 model,.