OV-106 Horizon, OV-107 Daedalus? Or vice-versa?

OK, this has always bothered me.

When Corvin and his team first arrive at NASA, Flight Director Gene Davis (William Devane) says that they will be flying a "new space shuttle," which we eventually learn is named Daedalus, the same name as Corvin's team. But we don't actually learn this until the launch scene; a technician tells Corvin and Hawkins, "Welcome to Daedalus," and then later real-life NASA announcer Lisa Malone says, "...liftoff of the Space Shuttle Daedalus..." We don't see the name Daedalus on the orbiter itself until it's in orbit (the shots conceal the shuttle's markings, but you can almost make out the name Discovery on the forward fuselage while the stack is on the launch pad).

Now, that the "new space shuttle" (presumably OV-106) just happens to have the same name as Corvin's team from 1958 seems like an incredible coincidence. Leave aside that it contravenes NASA's orbiter naming policy, as there is no famous historical ship of exploration called Daedalus. Even in the movie's fictional universe, if this -is- a coincidence, it's never mentioned; if not, it's never explained.

During the training scenes, the astronauts can be seen wearing mission patches on their clothing that show the name Horizon; in some shots you can see all of the astronauts' names (CORVIN HAWKINS O'NEILL SULLIVAN GLANCE HINES) inscribed on the outer edges of the patch, meaning this is meant to be an actual mission patch. (There's a good, clear shot of it, worn by Glance (Loren Dean), in the scene where Glance argues with Corvin right after the latter gets out of the water tank.) In addition, Hawkins identifies the orbiter as "Horizon" during the landing simulation scene. But when the launch scenes arrive, the shuttle is now named Daedalus and there's a different mission patch on the astronauts' spacesuits.

OK, what happened here? Was OV-106 Horizon re-named Daedalus in honor of Corvin's team right before the mission? Or are these two separate fictitious vehicles, OV-106 Horizon and OV-107 Daedalus? Or maybe it's the other way around; Davis mentions before the training starts that they'll be flying a "new space shuttle," which we guess is Daedalus, but if the first mission patch says "Horizon" then that's probably the one Davis was talking about; maybe the older orbiter Daedalus was substituted at the last minute?

It could also be that Horizon is just a placeholder name for a fictitious (within the fictituous universe) orbiter, used as a generic name for the shuttle during training exercises. This seems unlikely, and it certainly wasn't NASA's practice to do that, let alone design and produce separate mission patches for the training and the actual mission.

Now, it certainly seems likely that this is the result of, for example, a mix-up between the costume department and the visual FX house, where the former was under the impression the shuttle would be called Horizon and the latter thought it would be Daedalus, and either the scenes with the Horizon patches had already been shot or the CGI shots of the orbiter Daedalus had already been produced and they had neither the time nor the money to re-do them. I've never heard or read an explanation for this and the screenplay basically ignores it. It just seems odd that no one mentions the incredible coincidence of the "new space shuttle" having the same name as Corvin's team, or in the alternative, that there's no scene where it's announced or mentioned that the orbiter will be renamed in their honor.

It seems highly unlikely that NASA would rename an existing orbiter; if nothing else, the cost of remarking the name on the wing and forward fuselage, as well as changing all the signage and other logistics at KSC and elsewhere, would not be worth it. All six orbiters were named long before they were completed. (Although the prototype OV-101 was originally to be named Constitution, the change to Enterprise was made before its completion and it was never referred to by the former name; NASA formalized the naming process after this.) The "new" orbiter that Davis refers to is nevertheless a month away from being ready to launch, meaning it can't still be under construction at that point.

So, which is it? Is it just an incredible coincidence that Corvin's team and NASA's new space shuttle have the same name? Was the shuttle Horizon renamed Daedalus in their honor? If Horizon and Daedalus are two separate vehicles, which one is the "new" one? Or does the shuttle Horizon not exist at all?