As viewed from the perspective of iOS, what is Mac OS X, really?
Is it the supercharged, full-featured version? That was more the case before the introduction of iOS4 than now, following that milestone. There is probably still an argument to be made for this view, but not as strong an argument as before. The biggest remaining difference is that Mac OS X handles a multi-window environment and full-blown multitasking. On the other hand, it doesn't yet handle touch events out of the box.
Is it the parent, with legacy issues? Parent, maybe; legacy issues, not so much. Most legacy issues in Mac OS X have already been dealt with. The biggest remaining one is probably the file system, HFS+, which dates back to later versions of the original Mac OS.
Is it the older, bigger brother? As a metaphor, this one actually works pretty well. Mac OS X has been around longer, is quite a bit more massive, and optimized for completeness as well as for performance, as measured both from the interface-response perspective of the user and with regard to battery life.
Being optimized for completeness means, among other things, that it supports a wide variety of hardware. A single installation disk can be used to install Snow Leopard on any of dozens of Mac models, with varying CPUs, GPUs, support chips, monitor resolutions, etc.
It also means that new features that aren't tied to a touch interface, or to one of the special capabilities built into the iPhone and other members of the iOS family, are likely to appear in Mac OS X first, especially if they involve a large amount of code/resources, or place a significant burden on the hardware.
So you could think of Mac OS X as being the extended version of iOS, or, given that it runs on more powerful harder, maybe the extreme version.
To come back around to the question of rebranding, "iOS Portable" (or Mobile), "iOS Desktop", and "iOS Server" works very nicely, except that it might begin to be confusing if you have laptop computers running "Desktop" and desktop computers or set-top boxes or tablets too large to carry around running "Portable" or "Mobile".
On the other hand, "iOSx", with a small 'x', no longer a Roman numeral, would also work, unusually quietly as such things go. Combined with separate versioning (iOS 4.x being contemporary with iOSx 10.6.x), it sufficiently distinguishes the products, while making it very clear that they are fundamentally variations on the same basic design.