Led Zep’s plane (sort of), The Starship:
Mother of all flying machines The Starship Enterprise.
Kee Bird and Glacier Girl, famous for getting stuck in Greenland’s ice.
The Laden Maiden (which I have been in)
The Gimli Glider.
The Good Ship Lollipop.
Yes, it was an airplane, not a boat.
And here’s a listof other B-17s either on display, in restoration, or flying from our friends at Wikipedia.
Spirit of Texas Flown by H. Ross Perot Jr. and Jay Coburn this helicopter completed the first circumnavigation of the world by helicopter
Chicago First plane to complete a round-the-world flight from April 6 to September 28, 1924
Polar Star Flown by Lincoln Ellsworth, this plane completed the first trans-Antarctic flight in November 1935
On a more serious note, the Space Shuttle Enterprise, along with her various siblings, such as Columbia, Challenger, Discovery, Atlantis, and Endeavour.
Admittedly, they didn’t make very good airplanes, but then again, what they were designed to do, they did better than most other planes could hope to.
So I’m reading this thread, just hoping no one mentions the Gimli Glider so that I can do it, and what do you know, post #30… I got to it in 2009, so I never had a chance. 
The Pregnant Guppy was a single variant of the Boeing 377, named because it looked like, well, a pregnant guppy.
Not quite meeting the OP’s criteria, but interesting nonetheless:
The Pregnant Guppy is the inspiration for the handful of Super Guppies and the two Mini Guppy planes.
I’m not sure if they have individual names, but the Airbus Beluga is interesting because “Beluga” was originally an unofficial name for the Super Transporter. It became so popular that Airbus changed the name, though it applies to 5 aircraft, not just one. Similarly, there are 4 Dreamlifter (747 Large Cargo Freighter) airplanes.