Can I install Windows 7 in A:\ or B:\ partition names?

Drive letters, such as A: B: C: are not partitions. Partitions are logical divisions on storage media. Drive letters are logical assignments to a file system made by the OS. Drive letters can be removeable media, hard disks, and other parts of a file system. Windows will reserve the A: and B: drive for floppy disks, however you can assign other volumes to A: and B: if you desire in disk management.

I would stick with C: for compatibility reasons, as you suggested. I'm sure that lots of programs out there just assume that the primary drive on Windows machines is C:, just like some programs assume that all Windows machines have the same path for My Documents or other common folders. I've definitely had problems with programs opening "Save as..." dialogs in nonexistent folders and either generating error popups or creating unwanted directories.

Sure, it's the programmer's fault, but you're going to be the one stuck with software that doesn't work, so....

That said, I agree with the contents of Keltari's answer.

As other pointed out partitions and drive letters are not the same thing.

In Windows 7 if you go to [Control Panel] > [Administrative Tools] > [Computer Management] > [Storage] > [Disk Management] you will see all your partitions (even optical drives, floppy drives, and flash drives).

If you right click on a partition/device there is an option [Change Drive letter].

You could make your "Windows" drive A:, your CD ROM P: and your USB drive: Z:.

Now before you go crazy. There is no good reason to do so. Programmers SHOULD reference the boot partition by variable thus if you change it then the program will still work but programmers are often lazy. They may hardcode their application to look in C:\WINDOWS\SYSTEM32 for example. They shouldn't but some of them do. If windows isn't on C the application is going to die.

Partition =/= drive letter. Drive letters are merely labels. Something that helps us humans relate to computers. Windows sees it as a series of devices and partitions. Nothing more.

AFAIK since Windows Vista the system partition always gets "C:" independent of the drive letter you installed it onto.