You can easily pass it as an environment variable
docker run .. -e HOST_HOSTNAME=`hostname` ..
using
-e HOST_HOSTNAME=`hostname`
will call the hostname and use it's return as an environment variable called HOST_HOSTNAME
, of course you can customize the key as you like.
note that this works on bash shell, if you using a different shell you might need to see the alternative for "backtick", for example a fish
shell alternative would be
docker run .. -e HOST_HOSTNAME=(hostname) ..