Hello Arjan,
Yes this is without a doubt possible. This is a very common request.
You can use Dynamic Registration to use a Display after message to display the details they provided after submitting the registration form.
You can go to Module Configuration -> General Settings and check the box -> Display Message to user after initial Registration.
Then you need to go to Module Configuration -> Module Layout / Javascript / Stylesheet -> Header / Footer / System Messages, then from the combo box/drop down box select the "Display After Registration message". You will be presented with a WYSIWYG editor that you can provide tokens in to make it Dynamic to each user.
If you have any questions at all please let us know by emailing us at dnnsupport@datasprings.com
Thanks,
Ryan