The name Picasso and the new registry number were derived from the 2006 remastered version of this episode. In the episode as originally aired, the shuttle was named simply Shuttlecraft 1, and was a re-use of the Enterprise shuttlecraft Galileo that appeared several times in recycled footage to represent other shuttles throughout TOS.
The Picasso was named after Pablo Picasso, a 20th century artist from Earth. Ironically, the real Picasso was not particularly impressed with space exploration. When asked about the Apollo 11 moon landing, the day after it occurred, Picasso was quoted as saying "It means nothing to me. I have no opinion about it, and I don't care."