Your app icon and its social sharing image are different things. A sharing preview is described by tags in the page's HTML, including og:title, og:description and og:image.
Use your own image
Give the builder your image and ask it to set the sharing tags in the app's HTML. Use an image that visitors can open without signing in. Ask it to update the Twitter card image too and keep both descriptions consistent.
The platform can supply an automatically generated sharing image. Its replacement logic preserves a custom image URL rather than replacing every image with the generated one. Put your chosen image in the actual HTML metadata; changing an image component on the page alone does not set the share preview.
After a remix or rename
A copy can inherit titles, descriptions and sharing tags from the original app's files. Ask the builder to check the page title, social title, description and image together. Renaming one label does not necessarily update all of them.
Check the published result
Publish the change, then inspect the live page's HTML and open the image URL. Use the social network's preview/debugging tool to request a fresh read if its preview still shows the old image. A correct browser tab title alone does not prove that a social crawler sees the new metadata.
Builder changes use credits. Test the address you actually share, including the custom domain when you use one.
Different previews on different domains
The built-in sharing image is configured for the app. It is not a per-domain image setting: multiple domains serving the same app normally share that app's image and source metadata.
Changing a tag with browser JavaScript based on the hostname does not establish what a social crawler receives. If you need different previews for different addresses, first inspect the raw HTML response on each address and confirm a supported way to return the different tags. Do not assume that connecting another domain creates separate content or a separate sharing-image configuration.
Publish the change, check each public URL and allow for the social network's cached preview. The app-level image setting alone cannot promise distinct previews per domain.