Using Mattermost Within a Company Network

This is not so much of a mattermost question actually. You need to make sure that all other machines in your network can actually resolve the hostname of wherever mattermost runs. You can check if it does by pinging the node for instance. Here's the difference between a host that can and cannot be resolved:

[root@master walter_mattermost_config]# ping gitlab.olindata.vm
PING gitlab.olindata.vm (10.20.1.50) 56(84) bytes of data.
64 bytes from gitlab.olindata.vm (10.20.1.50): icmp_seq=1 ttl=64 time=0.349 ms
64 bytes from gitlab.olindata.vm (10.20.1.50): icmp_seq=2 ttl=64 time=0.361 ms

[root@master walter_mattermost_config]# ping mattermost.olindata.vm
ping: unknown host mattermost.olindata.vm

How to add dns entries I'll leave up to your google skills