Hello there, Flynn.

In QuickBooks Desktop, you can only change the customer linked to a job. You'll want to create another job to link it to your customer.

Here's how:

1. Click the Customers menu.
2. Go to Customer Center.
3. Click New Customer & Job, then choose Add Job.
4. Fill in the necessary fields.
5. Click the CUSTOMER drop-down, then choose the customer.
6. Click OK.

Please check the screenshots below.

Feel free to visit the Community if you have other concerns.