There is a widespread urban legend in the Windows community that Dave Cutler chose the name "Windows NT" (WNT) because if you subtract one from each letter you get VMS, which is the operating system that Dave Cutler worked on before he came to Microsoft.
However, that is not true. Neither did Cutler choose the name (it more or less emerged by accident) nor was the name WNT (it was, in fact, "NT OS/2", because at that time, the idea was still to build the next generation of OS/2 – Windows wasn't even in the picture). NT also doesn't stand for "New Technology".
Dave Cutler was hired by Microsoft to build a next-generation operating system for the PC. At that time, Microsoft's most modern OS was OS/2, built jointly by IBM and MS. And so, to MS, "next-generation" naturally meant a new version of OS/2. (Windows was just seen as a GUI for DOS, that would soon be replaced by a real OS.)
At DEC, Dave Cutler had worked on VMS. One of the problems with VMS was that a lot of it was written in assembly, and that it was fairly monolithic. Both meant that it was somewhat hard to port to other platforms. When he was tasked to write a successor to VMS, he changed all of that; while he liked the abstractions and style of VMS, he didn't like the implementation: he wanted to write it in a highly modular style, and he wanted to do it in C – basically a cleaned up and modernized re-implmentation of VMS. DEC soon lost interest in his project, and effectively mobbed him out of the company, which is how he ended up at Microsoft, where he was able to implement his ideas. (Which is why NT looks so similar to VMS: it's essentially the version of VMS Cutler always wanted to write but DEC didn't allow him to.)
So, Cutler was writing a new version of OS/2. At that time, it was not at all clear, what exactly a "PC" was and that the i386 would win out. Intel was experimenting with RISC processors, Microsoft was experimenting with MIPS processors, IBM was doing the PS/2 and later also the PowerPC, DEC's Alpha was around the corner. Building an operating system for only one of those platforms would have been a huge and dangerous gamble. So, the new OS/2 would have to be highly portable. In order to ensure maximum portability, Cutler tried to find the strangest, most PC-unlike architecture possible. And he found the Intel i860. The i860 was 64 Bit, the i386 32 Bit. The i860 had plenty of registers (32), the i386 only 8. The i860 is RISC, the i386 CISC. The i860 has a VLIW architecture. It had a SIMD unit on the chip (that would later become the inspiration for the MMX SIMD instructions on the Pentium MMX). It exposed its pipeline to the software, so that all the scheduling decisions that the i386 makes on the chip, would have to be made by the compiler (this was the inspiration for the EPIC architecture of the Itanium). And it had one of the strangest memory models ever.
In short, it was the perfect target for a highly portable OS: if you developed and tested on the i860, you could port it almost anywhere. So, that's what Cutler did.
There were two versions of the i860: a cheaper, simpler one called the XR and a faster one for SMP machines called the XP. Except MS was working with early prototypes and the marketing names hadn't been chosen yet, so they were simply known by their Intel codenames: N10 and N11.
The operating system that Cutler was working on, was codenamed Portasys, because of its portability. However, internally they didn't call it that: they were building it for the N10, and they were building a version of OS/2, so in conversations they simply called it "OS/2 for N-Ten" or "N-Ten OS/2", and because programmers are lazy, that quickly got shortened to "NT OS/2".
Then, two things happened: MS hadn't actually bothered to tell IBM that they were building their own version of OS/2. When IBM became aware of the fact that the new OS/2 was actually quite different from the old one, IBM and MS had a falling out and the joint development of OS/2 ended.
The second thing that happened was that Windows 3.0 took off beyond everybody's wildest dreams.
That's when MS changed directions 180°. And now the modular design of NT OS/2 came in quite handy.
In NT, there is a clear distinction between the kernel and what is called a "personality". Usually, the kernel's job is to abstract the hardware and present an abstraction to userland. In NT, these responsibilities are split: the kernel abstracts, and the personality presents the abstraction to the userland. Well, actually, the personality does not present the abstraction, it presents an abstraction; there can be multiple personalities.
At this point in our story, NT looked like this: there was the NT kernel, on top of the NT kernel was the OS/2 personality, and on top of that was the OS/2 Presentation Manager (GUI). The filesystem was HPFS. Because of the personality abstraction and the ability to run multiple personalities at the same time, it was now very easy to keep the system running while at the same time adding a Windows personality. Once the Windows personality was complete, Presentation Manager running on top of OS/2 was replaced with the Windows UI running on top of Windows. HPFS was renamed to NTFS and some tweaks were made.
And then some marketing guy somewhere decided that that "NT" moniker was actually kinda cool, but the "OS/2" thing had to be replaced with "Windows" and it sounds better the other way around ("Windows NT" instead of "NT Windows"). And when he was asking what NT stood for, they told him that it didn't actually make any sense because they weren't doing an i860 version any more, and so he retroactively created the backronym "New Technology".
That's how it became WNT. And, as you can see the letters "N" and "T" were chosen by chosen by Intel, the letter "W" was chosen by fate and the ordering of the three letters was chosen by some marketing guy, so there is simply no way that anyone could have consciously chosen them in relation to VMS.
And, by the way: Arthur C. Clarke has always said that he never thought about "IBM" either, when he came up with the name "HAL". In fact, he said that if he had recognized that relationship he would have changed HAL's name out of respect to IBM with which he had very good working relationship.