Who decides to which side of the carrier the BFO will
heterodyne a CW signal.

For many SSB+CW transceivers, the maker of the transceiver decided on a
default sideband at manufacture time. Usually USB for rigs that are
capable of both sidebands.

For the oldest SSB equipment you don't get a choice of sideband:
14MHz and above comes out on USB, 7MHz and below come out on LSB, due
to the 9MHz IF + 5MHz VFO scheme.

I mean there must be convention, otherwise
we would have to find out on an individual basis

It doesn't matter as long as you're consistent between your TX and RX,
AND you make sure you're inside your band.

With most (all?) modern synthesized transceivers the frequency on the
display is that of the CW transmission in CW mode, but on older SSB+CW
rigs there was an offset (between a few hundred Hz and a few kHz)
between the dial and the actual CW transmission frequency (which was in
the sideband - the dial was calibrated to the suppressed carrier
frequency in USB/LSB). The offset was usually mentioned in the manual
(or in fancier rigs with RIT/XIT could be dialed in).

Tim.