start docker with customer system name and hostname

docker run --name david -h david-01 -it david/c6nodepm2yo /bin/bash

nJoy 😉

shows :

docker ps -a
CONTAINER ID IMAGE COMMAND CREATED STATUS PORTS NAMES
f4da454e156e david/c6nodepm2yo "/bin/bash" 12 seconds ago Exited (0) 3 seconds ago david
d5ec5101ba52 david/centos6:node "/bin/bash" 27 hours ago Up 26 hours 0.0.0.0:8000->80/tcp jovial_borg

and when connected :

[root@david-01 /]#