Yes, you can transfer a business name from one ABN to another.
You can transfer a business name by logging into or creating an ASIC Connect account by going to ASIC Connect. You will need to start a "cancel/transfer" process which will provide you with a transfer number. This number is then used to register the business name to the new ABN in the same manner as registering a new business name.
Patricia Holdings can transfer the business name for the same cost as registering a business name.