Vultr server install. What domain name should I use on my public facing machine when setting up OMV 5?

Please stick to one thread.

As you are asking this, I assume you do not have a own domain registered somewhere.

If you have the IP of the server, do a reverse lookup here: https://mxtoolbox.com/ReverseLookup.aspx

strip the hostname from the result and that's it.

Should not be related to your problem accessing the UI though.

if you are at the system type ip a to get the ip and try to access the ip in the browser. If vultr has a firewall in front of your machine, you have to open the ports (don#t know much about vultr)

Having a server in the internet looks easy these days, with all the guides around, but be sure you know what you are doing before putting sensible data on the server.