All Armenian citizens must have a registered address.
If a foreign address was specified in your citizenship application it will be automatically registered as your official address. If you want to register a local address (e.g. because you want your passport or your ID card to show "Armenia" as your country of residence) you will need to show proof that you reside in Armenia. It can be a certificate of ownership or lease of a residential property or the owner's consent to the registration. If none of these documents are available you may request the local police to make a factual check (normally takes up to two weeks) and confirm that you actually reside at the address in question.
If you are a male under 50 years of age, registering a different address may require you to register with another military office located in the new area of your residence.