We can merge fields in the Salesforce Messaging Component to greet using the agent’s name in Salesforce Messaging for In-App and Web Session.

Messaging Component:

Formula Template:

Hello {!$Parameters.MessagingSession.MessagingEndUser.name}, 
Thank you for waiting.
My name is {!$Parameters.MessagingSession.LastModifiedBy.CommunityNickname}, nice to meet you. 
How can I help you today?

I have used the Agent’s Nickname(CommunityNickname) to replace or mask or hide an actual agent’s name in Salesforce Messaging for In-App and Web Session.

To replace an actual agent’s name in Salesforce Messaging for In-App and Web, please check the following:

Replace an actual agent’s name in Salesforce Messaging for In-App and Web

Output: