Should you use Let's Encrypt for internal hostnames?

I will never understand the obsession people have with hiding their private server names.

If somebody gets any access to your local network, there are plenty of ways to enumerate them, and if they can't get access, what's the big deal?

I get that you may want to obfuscate your infrastructure details, but leaking infrastructure details on your server names is quite a red flag. It should really not happen. (Instead, you should care about the many, many ways people can enumerate your infrastructure details without looking at server names.)

One of the examples given wasn't a server name, it was leaking potentially confidential information via the domain olympics-campaign.staging.example.org - in many environments its fine if people know project names, but NDAs are a thing, and you could end up in hot water if you accidentally leak a partnership between two companies before it's been announced.

Well, if instead of making a lot of effort in hiding your names you just didn't, you wouldn't use a name like that.

Every single person that connects to any of your networks (very likely the sandboxed mobile one too) can find that name. Basically no place hides it internally. There is very little difference between disclosing it to thousands of the people that care the most about you and disclosing it to everybody on the world.

The other examples are better. Say a never-before-seen name appears, cisco520.internal.foo.bar. Suddenly, a well-formed email appears, “Re: Cisco Support Ticket #7779311” about some additional steps to provision your new appliance. It is trivial to automate that phish by crawling the CT log.