The program was called Apollo and the assembled launch vehicles were numbered by launch. But the orbiters and landers had their own names.
Here's Eagle returning to Columbia.
It's funny. While the Apollo craft obviously had a name, NASA never gave a name to the lunar module, simply calling it "the LEM."
They had to shorten that to LM, since the E stood for excursion and NASA didn't want anyone to get the idea that the lunar landing would be a vacation or picnic.
Ahem.....The Eagle has landed.
I think Neil Armstrong's LEM was named "Eagle".
But every module had a distinct, crew-given name like "Snoopy" or "Eagle".
As pointed out, the LEM was later shortened to LM. The Apollo name was for the program, not any vehicle. The capsule the crew was launched in was the CM for Command Module.
When in flight, but with either the CM or the LM and CM attached, the crew was called "Apollo" no matter what vehicle they were in. When the 2 spacecraft were flying separately, they used names as call signs (i.e. Columbia, Eagle).
The program was called Apollo and the assembled launch vehicles were numbered by launch. But the orbiters and landers had their own names.
Here's Eagle returning to Columbia.
The Apollo 11 Command Module "Columbia" carried astronauts Neil Armstrong, Edwin "Buzz" Aldrin, and Michael Collins on their historic voyage to the Moon and back on July 16-24, 1969. This mission culminated in the first human steps on another world.
The Apollo 11 spacecraft had three parts: the Command Module, the Service Module, and the Lunar Module "Eagle". While astronauts Armstrong and Aldrin descended to the Moon in "Eagle", Michael Collins remained alone in "Columbia". For 28 hours he served as a communications link and photographed the lunar surface. After reclaiming Armstrong and Aldrin from the ascent stage of the Lunar Module, "Columbia" was the only part of the spacecraft to return to Earth.
Transferred from the National Aeronautics and Space Administration.