I regard Kindle's as health hazards, so my knowledge is scant.
But Calibre should update the metadata in the format file (MOBI) when its Sent to Device, not sure why it wouldn't in this case - viz:
You could try using the Embed Metadata tool before sending, you'll probably need to add it to a toolbar/menu, or give it a shortcut, I have it set to Ctrl+E.
BR