If you are leaving Iceland, there are several bureaucratic matters that you need to address before your departure.
Places where you might have to de-register.
Þjóðskrá - Registers Iceland: Notify the National registry that you are leaving.
Bank: You should close your Icelandic bank account.
Tax office: The tax year is the calendar year. An individual subject to a limited tax liability must file a tax return to the tax office in the region where he lives, while staying in the country, not later than one week before he leaves the country.
Rent: You should terminate you rental contract, usually you must give 1-3 months notice (starting from the 1st of the month following the date when you inform them)
Utility services: Heat, internet, electricity services have to be cancelled.
Telephone provider: Notify your telephone provider and cancel you phone contracts.
Medical information: If you have enjoyed medical assistance during you stay in Iceland you are advised to go to your doctor (at your local clinic) before you leave in order to transfer necessary information to your next destination.
Post office: To receive your post, notify the post office about your change of address.
Unemployment: If you are unemployed you can transfer your rights to unemployment benefits to other EU/EEA countries