We said before that the store is basically a set of folders in a hierarchy. There is a function that will give us the unique identifier of the inbox: GetReceiveFolder():
result = store.GetReceiveFolder('IPM', 0)
inboxid = result[0]
The GetReceiveFolder() function actually returns two values: the unique id of the requested message class (IPM) and the message class that actually matched (IPM). There is not much point in explaining the exact meaning of these message classes since there is hardly ever any reason not to use IPM as the message class when you pass it to GetReceiveFolder().
Once you have that unique ID, you can use the generic OpenEntry() method of the store to open the object with that unique ID. In fact, OpenEntry() can open both folders and messages, purely depending on which unique identifier you request:
inbox = store.OpenEntry(inboxid, None, 0)
Now we have an open inbox object. Just like stores, an inbox also has a PR_DISPLAY_NAME property. You can get it in just the same way as the store:
props = inbox.GetProps([PR_DISPLAY_NAME], 0)
print props[0].Value + '\n'
This will show Inbox or your localized version of Inbox.