Custom filename when pasting an image from clipboard

You could create a plugin for the editor to achieve that. In JS there’s the onpaste event. These would be the basic steps:

1. listen for onpaste.
2. Find the closest heading element up the tree from the target element being pasted into.
3. Default to page/post title if no heading elements are found and then back to the default naming convention if all else fails.
4. Send the name you created based on that information back to server and trigger renaming the file with the PHP code you made.

creating an input box would be a little bit more indepth to do in gutenberg – but automatically naming them seems like it would be more ideal for you anyways.