Hi @Lutz Mahle ,
Hate to see you having issues with registering your phone number. It sounds like it may be a portal issue. Please following the instruction in the private comment below. In the meantime, you should still be able to file a billing support request where the team can get you over this last hump. Head over to Azure Support Options where you can create a new support request. You can use Microsoft account you intend to use to create the subscription to create the request.