Jen We aren't required to have a residence permit or any documentation to live here that he can use instead.
Keep in mind that just because the government of the country you're residing in does not insist on you getting a certain document for living there, it might still be required to acquire it for opening an account at bunq. The identity verification system is limited in that for security reasons it can only accept certain types of document. This restriction is not exclusive to people that have moved country, but for example also all Italians that sign up for bunq are required to get a plastic ID card, even though the Italian government does not strictly require them and some of them only have paper ID cards.
That being said, it's definitely the best idea to talk to a human from bunq about this like Thijs suggested. They will then be able to guide you and see if there are any exceptions to be made.
