Parent Theme Name?

I purchased a theme called serenityshop, and recently the creator updated the theme but changed the folder name to serenityedd, so when I update, I had to reinstall it as a new theme, I noticed that inside WP theme page, the serenityedd theme still appears serenityshop as the theme name.

My question is: I have a child theme made for serenityshop, should I update the name for parent theme to serenityedd?

Recap: The updated theme is inside a folder named serenityedd, but after installed, appears serenityshop for the theme name inside wordpress admin interface.