QB Issue Resolution:

I apologize but i am not sure i fully understand the question.  If you want to add custom fields to a customer record, you would turn on the custom fields in the “My Field Labels” area of company preferences (requires the pro version or multi-store).

But since you also mention discounts, i am thinking you might be looking for the location to add descriptions to the drop down on the discount window.  If that is the case, you can add them through the price manager tool (you will find that under Inventory).  Click on the Set Up Manual Discount button and you can add new discount names there.

Resolution for Issue 'How do I add/edit custom fields? When I select a customer, apply a discount, how do I add fields for where to assign the discount to?' available: Yes (Solved).
Source: Intuit Community forum.

How do I add/edit custom fields? When I select a customer, apply a discount, how do I add fields for where to assign the discount to?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

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