When I installed my first Raspberry Pi and enabled the Apple File Protocol (AFP) so that I could connect to its file system from my Mac, all was well. It defaulted to using it's own name "raspberrypi"
However, with two Raspberry Pi's on the same network, I needed to identify them individually.
All that is required is a file to be added to the file:
If you don't have one of those, simply create it:
sudo pico /etc/avahi/services/afpd.service
and copy and paste the following:
In the line beginning: <name replace-wildcards="yes">%h</name>
replace the %h with the unique name you have decided upon: