Assuming this isn't authenticated message?
In your inbound message flow you will want to associate the conversation with a participant, once that is done the name of the external contact will come though.
API put /api/v2/externalcontacts/conversations/{conversationId} will let you associate a conversation to an external contact.
There is a few things you will need, identifying the customer, validating they are that person, creating or finding the external contact, getting the communicationId etc. But assuming you have all that in hand, then above will then display the external contact name.
EDIT:
Community Rockstar Lawrence Drayton shared a good flow to get you started here:
------------------------------
Anton Vroon
------------------------------
Original Message:
Sent: 05-14-2025 19:15
From: Mahmoud hassan
Subject: How to change NO Name in Digital Bot Web messager


How to update no name with a variable like customer name that was taking during bot conversation with customer or how to update in general
Thanks
Mahmoud Hassan
#API/Integrations
#ArchitectureandDesign
#ConversationalAI(Bots,AgentAssist,etc.)
#Omni-ChannelDesktop/UserInterface
------------------------------
Mahmoud hassan
N/A
------------------------------