In reference to this Help document:
We would like to pre-populate the widget with a custom field. Can we set the field to be active across the entire organization? Will the Field ID change for each widget?
Yes, you can assign an external key to a custom field, so that you can refer to it across multiple widgets: https://app.agendize.com/book/76xxxxx854?test=myvalue
Please see screenshot below:
I hope this helps!