This is probably benign, the publishing server will pick up your servers hostname and use that as the gateway name.   This is probably fine unless you've customized this somewhere else.  Best practice is to set everything at install time, but understandable that this is not always possible.  On your TSIM server where publishing server is installed, if you run the psstat command and it comes back with "Started - Automated Mode" you're in good shape.

There is a config file where you can manually set this name, but it's not necessary if your Publishing Server is working and connected.

That's fine, you'd just need to manually publish every now and again.  Looks like you are in good shape.