The english terminology is not standardized. I can see why you object to “remove”, but i would be more relaxed and let people say “removed”.
In my opinion, “HHR - leaving the country” is the least ambiguous and matches the form name, but not concise. (However, it is confusing because if you are a dual national, you can enter Taiwan on your other passport(?) and you don’t have to leave the country. Also, this is not for someone who just leaves to go on a vacation. This is for someone who is intending to domicile in another country for at lear a year and probably a few years.)
“HHR - move out of the country” is a little more ambiguous.
“move out HHR” is probably the most concise and a good phrase for the action (verb). Then, you become inactive (noun) (i suppose). “Inactivate HHR” (verb) could also work, but that verb is not common in English. So “remove” (verb) would be appropriate because you are removed from active status. I.e., if you need something where you have to show your HHR (hukou), you won’t be able to. A person is removed in that sense.
Anyway, i don’t think there is any other meaning that could be given to “remove” or “cancel” besides the move out procedure.
I also don’t like move-out procedure because I think in Chinese there will be a term for “moving” your HHR from one address to another. So, having the english words of “move-out” meaning to exit the country (on a 2yr+ basis) and “moving” meaning to change HHR address is also confusing because they both use the word “move”.
The form is called 出境遷出申請書 which google translate calls “application for leaving the country”. So those phrases are unambiguous, precise, but long.
@newhere (above) quotes my recent post on this and the form I got from the HHR office in New Taipei in 2025. (Thanks!)
Naming and translating things is not easy, so until there is a standardized phrase, I think all of these phrases is fine. And also fine to ask for clarification.
I.e.
Are you leaving the country?
For how long? (Anticipated)
Will your home base (domicile) be in another country?
What are your goals? (wrt Health Insurance, Taxation, national pension, other government programs.)