If you have not disabled the conversation panel, you can further configure the data fields shown on the Intercom conversation cards in the Jira issue view.
From the Jira home screen click Projects (1) in the main navigation menu and select the project that you would like to configure (2). After the project page loaded select Project settings (3) in the left-hand menu then scroll down to find and click on Intercom integration. This loads the Intercom integration settings page.
Click the Conversation Panel tab (1). Locate the section called Visible fields (2) where you can configure what data is shown on conversation cards for different Intercom entities.
To configure fields, select the Intercom entity that you would like to configure (1). After that, you can rearrange the fields (2) in any order you like using drag-and-drop.
To make a hidden field visible select it from the dropdown (3) and click Add Field. If you wish to hide a field you can remove it by clicking the trash bin icon (4).