iPhone is confused with iMessages
It's possible that one of you is using the phone number to initiate a message, and the other is using an email address.  Starting from a blank slate, send a message, and have Niels reply, do you then have a single session, or 2?  If this is behaving oddly, try initiating the chat with both email and phone numbers, and see what happens.

Your recent contacts will likely show both messages from e-mail and phone number.  You might think that the iPhone should match and merge both conversations but in fact they remain separate for good reason.  Imagine you have an iPhone and an iPad, messages to the phone number only go to the phone, messages to the email go to both. It's a case of knowing how to reply. If it merged the 2, which would it choose to reply to?  It would have to choose the email address, as it's portable, the phone number isn't.  Any attempt to merge could leave one of your devices only getting half the replies, or the inability to reply if replying to an iPad from an iPhone that has decided to use the phone number as the primary contact choice.