https://en.wikipedia.org/wiki/Bockscar https://en.wikipedia.org/wiki/Enola_Gay
It seems like a big joke. Why would they make it seem so informal?
Crews were allowed to make up their own names for their plane and there was a painter who would come and paint images on the plane's side that were thematically appropriate. Enola Gay was the name of the mother of Paul Tibbets, the plane's pilot.
Bockscar was named after Captain Frederick C. Bock, the commander of the plane. His crew ended up not being the one to fly the plane to Nagasaki, it was the crew of a different plane that ended up flying the mission. So the name sounds more puzzling if you hear the name of the crew, whereas it would have an obvious origin if it had been flown by its normal crew.
Flying bombing missions was a frightening and deadly task, and a significant percentage of the young men flying these planes would end up dying in these planes. They picked the names to raise their spirits or laugh in the face of death or remind them of loved ones they might never see again. For example, Louis Zamperini, recently profiled in the biopic Unbroken, flew a plane that he and his crew named "Superman". Almost all of the names of these planes have been forgotten and were never historically relevant. But the two planes that carried the nuclear bombs will likely be remembered until the end of human history, due to the historical significance of their missions. The planes' names thus have a significance that was never suspected or intended by the namers at the time the planes were first named. Perhaps they would have chosen different names, perhaps not. Tibbets' mother is now immortalized, while Bock will be remembered as a footnote forever because of the name of a plane that flew a mission he wasn't a part of.