Jefferson Airplane.
‘Mystery S’. 
It lives again as a replica built to commemorate it.
Rolls up newspaper and smacks Rigamarole behind the head.
On the other hand Elvis had a Convair airliner called Lisa Marie.
There’s also the name of the plane that crashed with Buddy Holly and Richie Valence, American Pie… although of course that’s only a well spread urban legend since the plane didn’t have a name.
I’ve always wanted an Ercoupe called Putt Putt Maru.
.
Good one! 
The various STS Orbital Vehicles, better known as the “NASA Space Shuttle” (properly, the Space Shuttle System is the whole getup they launch from Florida, and not really a plane). It meets all the proper definitions of an airplane.
“The Sacred Cow” FDR’s USAAF plane, a modified C54 Skymaster, during WWII.
Braniff had a plane that was called the Great Pumpkin because it was painted entirely orange. They also had planes painted by Alexander Calder known as the Flying Colors.
All Pan-Am planes had names, Clipper Something-Or_Another.
Joe Walker named his planes Little Joe.
YS-11
Stardust
In general across the industry, the 727 type was nicknamed “the Pig”, while the 747 type was nicknamed “the Whale”. Of all jetliners, those are the only two types I ever heard of having generic nicknames.
At the carrier I used to fly for, all the 727s had unofficial pig-centric names. “My Hammie Vice”, “The Hamtramck Express”, “The Poland China Clipper”, etc. There was some guy who years ago had appointed himself the pig namer and would stick homemade name stickers on each instrument panel. Folks liked the names.
Eventually some humorless FAA man decided that these stickers represented an unauthorized and unapproved modification to the aircraft and lit a fire under our maintenance dept to remove all stickers immediately when found. They fought a seesaw battle for a couple years but eventually the stickers disappeared & the names began to fade from common memory. Then we got rid of all the 727s and now the names are gone forever.
Across the industry there are a couple of (in)famous very-unofficially named airliners; usually those which survived a near death experience.
There was a near-accident involving one of the first MD-11s, when the airplane didn’t want to let the crew land and it took some heroics to regain control from the automated systems. Nobody ever came up with an adequate explanation for what happened that day, and years later the airplane was known as Christine, in tribute to the cheesy horror movie of the same name.
I talked with an MD-11 pilot from the smallish carrier that ended up owning Christine. He flew that airplane a bunch and said it was common knowledge at his place that there was something just not right about that airplane; it wanted to go its own way just often enough to convince even skeptics that the weirdness wasn’t just confirmation bias.
There are a couple others, but I’ve been away long enough that the airplanes in question are now beer cans and the details are hard to find online & I don’t remember well enough to tell the stories ad lib.
Well you have the Bell X-1 and X-2 which broke the sound barrier, and the Skylanes Unlimited race planes that flu in 1946. The Skylanes Cobra I, with Jack Woolans at the controls, crashed into Lake Onterio(sp) just befor the 1956 Cleveland air races and Cobra II, with Alvin “Tex” Johnson at the controls that went on to win the race.
The Bell P-59 was the first American jet to fly. Jack Woolams was at the controls on many of it’s flights. On one of them he wore a Gorilla suit and was smoking a Cigar when the other non-jet planes would buzz this top secret plane.
Huh. Look at this shot of the nose art (which, btw, looking at it from this point in history, is in rather bad taste, I have to say). That cloud over “Nagasaki”… is it just me, or does that look rather a bit like… well, you know?
The Gold Bug.
Boeing names all their 747’s for cities prior to rollout. The first 747 is the “City of Everett” (so named because the 747 plant is in Everett, WA). I had a minor role in the some of the software for the first 747-400 (and attended first flight). I can’t remember which city it was named for, though. (Any PNW dopers know this?)
They may name other models as well, but I’m not aware of it.
[shameless brag] I have actually flown the “Chuckie”, a restored B-17. The owner let me take the left seat during a long cross-country flight.
To me it’s a famous name. 
[/shameless brag]
Missed the edit window.
I’d also include the Hacienda*, which holds the record for the world’s longest continuous flight. They were aloft from Dec 4th, 1958 to Feb 7th the following year. AFAIK, this record has never been broken. Here’s a picture of the plane that accomplished this. (Surprising, huh?)
*I know the name was that of the sponsor, but many sites refer to that as the plane’s name as well.