Existing Discount Names cannot be edited, but you could just duplicate the discount with a new one using the new name, and then delete the old one.
Also note there's currently a bit of a glitch in how our Discounts Editor screen displays discounts. This only affects how discounts are (or aren't) displayed there, but does not affect the actual discounts themselves.
When you select a Discount Name from the Current Discounts menu, discounts named using any non-alphanumeric characters (i.e., anything other than letters, numbers, and spaces) currently fail to display their actual Discount(s) saved under that Name.
Meanwhile, until our Devs fix that glitch, if you want to view/edit/delete an existing discount but can't load its settings by selecting its Discount Name from the Current Discounts menu, you can instead select All Discounts in that menu and find your discount in the list that will appear. We realize this may be a bit tedious if you have a lot of discounts, but hopefully that workaround will not be necessary for much longer.
This glitch appears to be a new bug that crept in when our Devs recently fixed another bug, where attempting to add a new Discount Code that already exists applied to the same thing -- e.g., duplicate codes applied to the Cart Item Total, or duplicate codes applied to the Item Unit Price of the same product -- would appear to succeed, but actually fail due to the duplication which is not allowed. Adding error feedback to inform users when and why a duplicate was blocked required some back-end programming changes that unfortunately introduced this new bug affecting display of existing discounts.