Since they are children they will not be asked for ID so I would put their chosen name on all reservations (except plane tickets if you fly). This way wherever they scan or an RFID picks up their name they will have their chosen names.
Also if you are staying onsite and ordering MagicBands you can have them printed inside with their chosen name.
Note that is just for fun, it will not be seen by anyone or any machine - just you. The MagicBand holds no information and has no brain - it connects to the info you put in
MDE - so it is important to register them on ticket and hotel by chosen name.