You can do this using REST API, JSOM or CSOM. I am not sure about from UI and SharePoint Designer. Have look on my REST API example.
- Upload your image in some Library.
l prefix to image/icon name. For example, your image/icon name is
my-doc-icon.png. Then after uploading to a library, change the name as
lmy-doc-icon.png. This is required. Otherwise it does not work.
Now update your Document library.
"ImageUrl": "relative url of your site/lmy-doc-icon.png"
You can use my SharePoint REST Client to make this update request.