In Finland, the biggest bank is actually just a group of local banks. So if I sign up for a bank account up north, I am the customer of the bank way up there, which is a separate legal entity from the bank down in the south.

Of course, if you do move and you want to apply for a new credit card, they will mail the card and paper work to any of the locations, so it's not that bad. And all of the banks in the group have an unified online banking system, no branch numbers needed. However, when I switched between the different banks, I had to get new login details for the online bank, which was kinda sucky.