How to clear names from "Add to cart as gift" dropdown box

[ILLRIDAH Jestyr]

There are names that are autofilled in this section that I would like to delete. How can they be removed? I've tried clearing everything except passwords from the browser but still no luck on the actual site. 

[Wulfie Reanimator]

That list comes from your browser, not the website.

If you're using Chrome, you can press Shift-Delete when you're hovering over an item of the list to delete that item.