How did they name the Apollo space missions?

Answer 1

PARTIAL ANSWER:

NASA Hq. Office of Manned Space Flight informed KSC, MSFC, and MSC of approved designations for Apollo and Apollo Applications missions:

1. all Apollo missions would be numbered sequentially in the order flown, with the next mission to be designated Apollo 4, the following one Apollo 5, etc., and
2. the Apollo Applications missions would be designated sequentially as AAP-1, AAP-2, etc. The number designations would not differentiate between manned and unmanned or uprated Saturn I and Saturn V missions.

   In a letter to George E. Mueller, OMSF, on March 30, MSC Deputy Director George M. Low offered two suggestions, in keeping with the intent of the NASA instruction yet keeping the designation Apollo 1 for spacecraft 012. NASA Hq. had approved that designation before the January 27 fire claimed the lives of Astronauts Virgil I. Grissom, Edward H. White II, and Roger B. Chaffee; and their widows requested that the designation be retained. The suggestions were:

3. Consider the AS-201, 202, and 203 missions part of the Saturn I (as opposed to uprated Saturn I) series; reserve the designation Apollo 1 for spacecraft 012; and number the following flights Apollo 2, etc., or
4. Designate the next flight Apollo 4, as indicated by Headquarters, but apply the scheme somewhat differently for missions already flown. Specifically, put the Apollo 1 designation on spacecraft 012 and then, for historic purposes, designate 201 as mission 1-a, 202 as mission 2 and 203 as mission 3.

A memorandum to the NASA space flight Centers, North American Aviation, and certain Headquarters personnel from the NASA Assistant Administrator for Public Affairs on April 3 stated that the Project Designation Committee had approved the Office of Manned Space Flight's recommendations and that Mueller had begun implementation of the designations.

On April 24, OMSF further instructed the Centers that AS-204 would be officially recorded as Apollo 1, "first manned Apollo Saturn flight - failed on ground test." AS-201, AS-202, and AS-203 would not be renumbered in the "Apollo" series, and the next mission would be Apollo 4. -from astronautix.com

Starting with Apollo 9 the crew was allowed to choose the call sign of the Lunar Module and the Command Module. The NASA Project Designation Committee determined the letter designation given to each flight. There were 7 flight designations from type "A" through "J" depending on the type of flight, i.e. Manned Lunar Landing was given the designation of "G".

Answer 2

The Apollo space missions were named after the Greek god Apollo, the god of the sun and light, as a nod to President Kennedy's goal to land a man on the moon before the end of the 1960s. The name Apollo was chosen to symbolize the "light" or "illumination" that space exploration would bring to humanity.