Can you apply a native DEPARTMENT field on a Customer record?

What do you mean? 🤔

Do Customers have a native Department field?

Nope

No I’ve always had to add a custom field for department on the customer (actually I’ve mostly seen it done on vendors as departments are usually used for costs) Then use a workflow or something to source it onto transactions

The use case here was to default the sales order Department based on Customer Department. Custom field plus script after customer sourcing was the approach we took