I don't think you can customize those icons... I've found that the only way to control what icon shows up is by using certain keywords in the sections name.
This is the list of keywords:
Honestly, their incompetence is just utterly despicable. This thread is 3+ years old.
To add to this list, "Text" is another keyword to asserts icons.
As always, it's important to remind Shopify and their engineers that they are really consistent at being inconsistent. Everyday my distaste grows for this company, it really is becoming pure trash.