If they're going to change their name, they will of course need to abandon the old trademarks.
Anyone claiming their old trademarks for new, will have the same problem of appropriating an indigenous name, and also the issue of approrpriating an abandoned name. Trademark law allows it, but it's not a good look for the newcomer.
For the domain, I would imagine a very long transition. There's a reason the current owner of asf.org still maintains that despite changing their organizational name away in 2010. If ASF starts using a new name and domain name today, I'd expect it takes about 3 years for everything to be fully moved, but old links will need to continue to work for some time after that. Some sort of annual review with a usage threshold would be appropriate... if there's negligable requests to http(s)://httpd.apache.org by 2034, you can remove the A/AAAA records. And a year or two or five, after there are no longer any DNS records for apache.org, it can be transitioned to another organization. Perhaps a transition can be arranged sooner if shared usage can be agreed upon; the new owner could use www while deprecated names continue to redirect.
Things like Maven and numerous other XML namespaces come to mind that can’t exactly move. Then there’s the tons of dirty money to be made by domain squatting apache.org even if all the technical problems were solved because the site has a reputation. It would be like Google changing their domain name and letting the old domain lapse.
Letting the old domain lapse is silly. Presumably, it would eventually be transfered to an indingenous organization, after its use had been nearly extinguished.
There would be references that outlive a naming transition, of course. But if you read a 10 year old book and expect all the urls to work, that seems highly optimistic. It's uncool to change URLs, but stuff happens.
For XML namespaces, I think it's reasonable to keep the existing ones, but a) when there's a new version, use the new domain name exclusively; b) after some time make provisions for publishing old versions under both domain names. My experience with XML namespaces is that they look like a URL, but there isn't always useful content at that url anyway, it's really just a string that's hopefully unique. It's been a while since I used them, but I seem to recall some useful namespaces being tied to domains that were no longer in use as well.
I've used active standards where the standards body had disbanded and no original sources were available... You had to rely on documents saved and shared. It happens, it's part of life. At least if the ASF changes its name, it will continue to exist.
It's work, perhaps a lot of work, but it's tractable. IBM changed its name to IBM, AT&T changed its name to AT&T, ASF can change its name to ASF. Heck, GMAC changed its name to Ally.
It’d be great if the Apache Nations wanted to control the domain name, but they’re still mostly concerned with basics like clean water and other government services.
Anyone claiming their old trademarks for new, will have the same problem of appropriating an indigenous name, and also the issue of approrpriating an abandoned name. Trademark law allows it, but it's not a good look for the newcomer.
For the domain, I would imagine a very long transition. There's a reason the current owner of asf.org still maintains that despite changing their organizational name away in 2010. If ASF starts using a new name and domain name today, I'd expect it takes about 3 years for everything to be fully moved, but old links will need to continue to work for some time after that. Some sort of annual review with a usage threshold would be appropriate... if there's negligable requests to http(s)://httpd.apache.org by 2034, you can remove the A/AAAA records. And a year or two or five, after there are no longer any DNS records for apache.org, it can be transitioned to another organization. Perhaps a transition can be arranged sooner if shared usage can be agreed upon; the new owner could use www while deprecated names continue to redirect.