Any operation that causes the app to interact with Intercom API (e.g. adding a comment that is being sent to Intercom, or transitioning an issue which adds a notification note to Intercom) will run as what we call the app user. The app user is the Intercom teammate who has/was logged in to Intercom when the Jira project first was connected to Intercom. This guide will explain how you can change the app user for any Jira project to another Intercom teammate.
You can find the currently configured app user for any Jira project by opening the Jira project's settings and clicking on Intercom integration (1) in the left-hand menu. If the Jira project is connected to Intercom you can find the app user Intercom teammate under Authorized with (2).
Open Intercom in your browser and click on your avatar in the top right corner, then click Logout (1).
If you would like to add a dedicated teammate for the app have a look at the Intercom documentation on how to add a new teammate.
Back in Jira, open the project settings and click on Intercom integration (1) in the left-hand menu. Then, click Revoke Connection (2) to revoke the connection to Intercom. Existing conversation links will remain in working order as long as you connect back to the same Intercom workspace.
Follow the steps on how to connect a Jira project to Intercom. When you are asked to log in to Intercom make sure to log in with the generic app user or whichever you want to authorize the connection with.