You can change the address name or description from a customers address through the address tab on the customer record.

If a billing schedule exist the Delivery Address name and Bill to Address name field do not automatically change to the new name. The delivery address and bill to address fields are correctly updated. When you invoice this billing schedule there is an error message thrown. You must manually thick the address field on header level to update both fields and proceed with invoicing.

Fix should automatically update both fields (Delivery address name and Bill to Address field).