How do I change the administrator details that show in the emails that are sent out from OpenAthens?

The details used in the automated emails are taken from the Account support information held in the system.
As an administrator for your organisation, you can update this as needed:

When you're logged into the admin site, you need to go to the Preferences menu, then choose Account:

Scroll down the page until you get to the Account support section:
Update the details (name, email address, phone number). Note: only the email address is a mandatory field.
Click on the blue Save preferences button:
You should get a notification that the changes have been saved.