I believe you are supposed to publish it on all your official paperwork too, eg business cards, invoices and so on. It is a control on you being legitimate.
Hi Louise, every Auto-entrepreneur's Siren number is freely available on the internet anyway in Google (usually along with your address and phone number too!). So no chance of keeping any of these details private!
you give it to just about everyone you deal with - it's nothing to keep hidden ;-)