I was able to find a few of these projects. There are probably more that I couldn't find any records of.
Two of the projects I found did not appear to be named Highlander for any reason beyond the fact that the person who chose the name was a fan of the movie.
Another project code named Highlander was an internal IT effort to simplify the way it did something really full of acronyms that I don't understand. ("Reduce the architectural footprint of the XYZZY QX Extranet.") There used to be something like five different systems for doing this thing (whatever it is), and they wanted to consolidate them down to one.
The project code named Highlander that people outside Microsoft will recognize is the one now known as Microsoft Account, but which started out as Passport.¹ Its goal was to provide single sign-on capability, so that you need to remember "only one" password.
The last example is kind of complicated. There was a conflict between two teams. Team A was responsible for a client/server product and developed both the server back-end software as well as the client. Meanwhile, Team 1 wrote an alternative client with what they believed was a more user-friendly interface. A battle ensued between the two teams to write the better client, and management decided to go with Team 1's version.
But Team A did not go down without a fight. Rather than putting their project to rest, Team A doubled down and tried to make an even more awesome client, which they code-named Highlander. The idea was that their project was engaged in an epic battle with Team 1, and the tag line There can be only one reflected their belief that the battle was to the death, and that their project would emerge victorious. This being back in the day when playing music on your Web page was cool, they even set up their internal Web site so that it played the Highlander theme music when you visited.
They were correct in that there was ultimately only one.
The bad news for them was that Team 1 was the winner of the second battle as well.
To me, the moral of the story is to keep your project code name humble.
Reminder: The ground rules for this site prohibits trying to guess the identity of a program whose name I intentionally did not reveal.
¹ The Wikipedia entry for Microsoft Account erroneously claims that the project was once known as Microsoft Wallet. That claim isn't even supported by the Web site they cite as a reference. The Web site says, "Microsoft Wallet has been updated to use Microsoft Passport technology." In other words, "Wallet now uses Passport for authentication." This is like seeing the sentence "Microsoft Active Directory uses Kerberos for authentication" and concluding "Kerberos was once named Microsoft Active Directory."