On the technical topic of renaming a domain of a Lemmy server… I think it is worth experimenting with the code.

This is unfortunately only possible if you still own the original domain. Think about it this way: if you could migrate domains without proving you own the original, then what's stopping a bad actor from migrating any domain they want? Keep in mind that Federated servers rely on DNS to verify who's who -- they don't have a backup system for deciding trustworthiness.

Yes, there's no technical reason Lemmy has to rely on DNS to establish trust (aside from the fact that changing this would require a massive rearchitecting effort), but why shouldn't it? It's possible to switch to a different trust system (i.e.: public/private keypairs), but that doesn't actually change the nature of the problem -- people can still lose control of the private key and blow the whole system up (and, arguably, this is a lot more likely to happen than permanently losing a domain).

At minimum, I think it should be an option to try and keep the same login/passwords for users from the old install of Lemmy.

So, login credentials aren't actually tied to the domain name at all. A user like example@lemmy.ml is simply known as example to the server internally. The server doesn't particularly care if it lives at lemmy.ml or microsoft.com -- if user example shows up and gives the right password, they're allowed to log in. What I'm trying to say is that -- assuming that the user database isn't destroyed -- login info would probably carry over without any special effort needing to be taken at all.

But even that could prove tricky if a particular domain changed underllying ownership more than once - and user@domain became rewritten by an entirely different person. I guess in the real-world people do often get mail for previous residence of a house.

The identity problem you allude to is not exclusive to this scenario. Let's use lemmy.ml as an example: where did the domain come from? The Mali government. Does this mean that the Mali government owned lemmy.ml before it became associated with the Lemmy project? At the risk of oversimplying: yes, pretty much! Prior to 2019, the government of Mali could have created "fraudulent" Fediverse posts under your username, /u/roundsparrow@lemmy.ml.

With that being said, it's kind of a silly concern. Despite being partially distributed, Lemmy is not a read-only database (i.e.: not a blockchain). There's nothing stopping the current domain owner from more-or-less completely undoing vandalism from a prior domain owner by simply asking the other federated servers to delete that fraudulent content. Keep in mind that the domain is not the server; the original operator keeps all of the original data even if they lose the ability to host that data under the original domain.

My biggest concern is legality because Lemmy claims to support privacy. I honestly think it’s a bad idea to claim privacy because you run into so many problems. If the user never knows that their lemmy instance changed names and can’t find it again, etc.

This is not a problem unique to Lemmy. If Google forgets to pay for gmail.com, then suddenly a lot of email addresses become untrustworthy. This isn't a privacy issue because your old emails don't leave Google's servers. It is a trust issue, however, since the new owners can now impersonate any gmail.com address and receive any new email that was intended for the original owner.

Not to downplay how catastrophic this scenario would be... but I don't think there's any law on the books which would legally obligate Google to operate gmail.com until the end of time. Nothing lasts forever and eventually gmail.com won't be controlled by Alphabet Inc. anymore -- that's just how time works. Those bothered by this uncertainty can instead choose to host their own mail server (or Lemmy instance) on their own domain -- this won't last forever, either... but at least you're in control now.

Especially on technical topics, 15+ years of having Reddit keep messages from deleted user accounts offered a lot of great search engine hits. With Lemmy, a person moving to a different instance and deleting their account, so much content is going to get black-hole in favor of 50 instances having copies of a meme post or trivial website link - and solid original content (often in comment discussions) gets removed.

~~Just FYI: Much like Reddit, comments continue to exist even when the author deletes their account. The user must explicitly delete each individual comment before deleting their account if they want it all taken down.~~ EDIT: This is not actually currently the case, though as far as I can tell the stated intent is to prefer anonymizing comments over deleting them when deleting an account (source). I don't really get this complaint in the first place, actually... surely both kinds of content would get lost when a user deletes all of their data, right? There's no button that says "delete all of my stuff, except for the shitposts".