This can be done by adding a custom field in the pass design. You can then populate this field when you enrol the member (or create the coupon).
To add a custom field that is different for each member, please follow the steps below:
Edit your design & add a new field of type Single Line Text.
Make sure the checkbox "This field value is different per individual pass" is checked - this allows you to dynamically set the field for each member. If you do not check this box, the same data will show for each member (this might be the desired behaviour)
Now when you enrol your member through one of the below options you can populate the field:
PassKit provided public enrolment form: field can be added to the enrolment form via "Your Project" >> Distribution >> Enrolment Form.
As an admin in the web portal: you'll notice the newly added field now appears when clicking the "Add Member" button.
The PassKit API: details on using the API with custom data can be found here: https://help.passkit.com/en/articles/3991200-using-custom-fields-with-your-membership-or-loyalty-program
Zapier: you'll notice the newly added field now appears when you use the enrol or update member zap.