I prefer to assign an external name to an internal device and grab a free SSL cert from LetsEncrypt, but using DNS challenge instead as internal IP addresses aren't reachable by their servers.
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Yes, I sometimes think about that, but have come to the conclusion that it's not likely to make any difference. If someone is trying to infiltrate my home network, then it's not going to really help them to know internal IP addresses as by the time they get to use them, they're already in.
I don't think the publishing of host names was mentioned as a concern for small home networks, but more for larger organisations that might be subject to a coordinated break-in or simply have trade secrets¹² that might be hinted at by careless naming of resources.
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[1] Their next big product/enhancement, as yet unannounced even within the company, for instance.
[2] Hmm, checking what is recorded against one of DayJob's domains I see clues as to who some of our clients are. Not really a significant issue for security at all, but I know at least some of our contracts say we shouldn't openly talk about that we provide services to that client³ so I'll drop a message to the ISC to suggest we discuss if we need to care about the matter…
[3] Though that is mostly in the form of not using their logos in our advertising and such.