Make sure "use author sort for author" is checked in the MOBI/AZW3 output preferences.
Since calibre cannnot change the metadata of books already on the device, you will have to resend all the books, but you can just overwrite them with calibre (assuming the send-to-device filename template remains the same).
...
Alternatively, you could do something involved using the command-line ebook-meta.exe tool to modify the metadata of the actual ebook files. But really, why bother -- resending is faster.