I’m not aware of a prescriptive Cisco document that answers the question as you have posed it. This is mostly a generic SIP RFC3261 question; the IP PBX would need to send the identity information in a SIP header, most commonly P-Asserted-Identity (PAI) from RFC3325.
The exact message that is conveyed in depends on the behavior of the IP PBX. For example, the PAI header for the consult call leg would likely be phone A. When the transfer is completed, I would anticipate a reINVITE with an updated PAI header depicting new connected party information.
The great thing about SIP is that it’s all plain text and easily readable. Pull traces or a PCAP of a call and just read through the SIP dialog to see what happens.