Question
When multiple agents assist on a chat, how does Zendesk know who to assign the ticket to? Can I configure this?
Answer
The answer to this depends on how your account is set up.
Standard agent interface
In the standard interface where Chat and Support are completely separate, you are able to configure whether the first agent to assist or the last one to assist has the ticket assigned to them upon creation. This option is accessed from Settings > Account > Zendesk Support tab in the Chat dashboard.
For more information on that setting, see this article: Setting up live chat in Zendesk Support (standard agent interface).
Agent Workspace
In Zendesk Agent Workspace, the ticket will start with the original agent that served the chat and change based on the Assignee field in Support. If you wish to transfer the chat to someone else, simply update the assignee field on the ticket.
For more information, see this article: Serving chats in Zendesk Agent Workspace