Re-naming a theme/child theme whilst maintaining updates

You should not store an exact copy of the Divi theme in your child theme, there is little point to that.

Your child theme stylesheet will reference the parent theme directory name in the template attribute within the header of your stylesheet:

/*
 Theme Name: Your Child
 Template: divi
 //shortened for brevity...
*/

The parent theme will load resources, in particular assets like CSS, JavaScript and images where by the path includes the parent theme name:

http://example.com/wp-content/themes/divi/style.css
http://example.com/wp-content/themes/divi/script.js
//etc...

If you want to completey hide the fact that you are using “divi” as your parent, you can rename the directory to something of your choosing, e.g. from divi to custom-parent.

Then you can open the Divi stylesheet and rename all references to “divi” and replace it with something of your choosing, again e.g. custom-parent or similar. Slugs for slugs, titles for titles.

You might want to use a grep tool to search and replace public instances.

If you do this, anytime Divi has a parent theme update you will need to rinse and repeat the process.

There are probably other things you can do like filtering paths and so forth.

…but honestly why bother?

If I look at the source of your site, I’d be able to tell, if I wanted to, if you are using Divi or some other site builder often by the classes, IDs and other markers the framework injects into the DOM.

The purpose of your child theme is to extend the parent theme so that it the parent meets your needs, often, becoming your own creation. Who really cares what framework you use as a means to an end?