A person is considered domiciled for tax purposes in the state where they have a tax obligation on all their income, whatever the source of that income. In general, tax domicile is considered to be the state in which an individual resides for a total of 183 days or more in a 12-month period.
That being said, tax domicile depends on the laws of each state and the definition may vary. If you are unsure, please contact a tax advisor or the tax authorities in your country.
Note that your TIN is not the same as your Icelandic Id. No. but a special tax identifier issued by the state where you are domiciled for tax purposes. You should find information about your TIN on the website of the tax authorities in your country.