mDNS

Multicast DNS (mDNS) is an alternative to traditional DNS for LAN-local name resolution. DNS queries are sent by multicast, and the node with the name being queried responds.

On linux, avahi is responsible for mDNS. avahi-daemon runs by default on some(?) distros, responding to queries for <hostname>.local.

You can start more instances to respond to requests for other hostnames too:

IFACE="eth0"
ADDR=$(ip addr list $IFACE | awk '/inet / {print $2}' | cut -d/ -f 1)

function _term {
  pkill -P $$
}

trap _term SIGTERM

avahi-publish --address -R $NAME1.local $ADDR &
avahi-publish --address -R $NAME2.local $ADDR &
avahi-publish --address -R $NAME3.local $ADDR &
avahi-publish --address -R $NAME4.local $ADDR &

wait

• Painfully Obvious → Using mDNS aliases within your home network
• Avahi how to assign several .local names to same IP - pi3g.com
• Multicast DNS - Wikipedia