Hello @Waclaw Michno ,
Thank you for your post! I have done some additional research into this inquiry and found the following document here with more information on how to update the contact information for an Azure Billing Account.
In this case, you will want to pay special attention to the Sold-to address and Bill-to address where the sold-to address refers to the address and contact information of the organization or individual who is responsible for a billing account and is displayed in all the invoices generated for the billing account and the corresponding steps can be found here if this is an Microsoft Online Service Program (MOSP), there's one bill-to address, which is displayed on all the invoices generated for the account. Otherwise, for a billing account for a Microsoft Customer Agreement (MCA), there's a bill-to address for each billing profile and it's displayed in the invoice generated for the billing profile which can be found here.
Meanwhile, you can find the instructions for updating the sold-to address per the following section here in the same document.
Please let us know if you have any further questions or concerns and we are more than happy to assist.
Thanks!
Carlos V.