I forgot to mention that my deposit was only 1000 euros! So yeah I feel this is wayyyy to intrusive for such a small amount of money, while my bank, Chase, does not ask that much question when I transfer far larger amounts.
I checked what the threshold figure is for triggering a suspicious activity report, and it's 1000 according to this website. I think the questions you were asked would technically be called Customer Due Diligence data gathering. However, they do seem intrusive.
http://eulawanalysis.blogspot.co.uk/2015/09/the-new-eu-anti-money-laundering-legal.html