How does the Linux filesystem on Android get mapped to "Computer\PhoneName\Phone" on Windows 7? I am trying to figure out, when I use adb shell I see a filesystem with directories such as /storage/emulated/0. When I connect my Android phone to Windows 7 I see something like the following folder: Computer\JohnDoe(GT-I9301\Phone.

I would like to understand how the Linux filesystem gets mounted under Windows. Does Windows mount only a specific part of the filesystem or does it reorganize everything into a new view?
By default, when connecting your device it gets mounted via mtp. Our mtp tag-wiki gives some details on this; basically, only parts of the device's storage is exposed – usually only the SD card(s).

In easy terms, you can think of this as something similar to your "Windows Shares", where you define directories to be available over the network (with the latter being an "USB network" using MTP): Android would "hand" it the SD card as "mount point" (in case of multiple SD cards, like one internal and one "physical", that would make two items). According to the protocol, everything below that should be shown as-is, like when mounting a remote drive. I don't know how Windows is supposed to name the "entry points", but it shouldn't re-arrange things below them. Your Computer\JohnDoe(GT-I9301)\Phone entry most likely reflects your internal SD card (/storage/emulated/0).