How to change database entries due to theme change

It all depends on the two themes. Generally speaking, the intent in WordPress is that if you switch your theme, you don’t lose functionality. However, some themes do have built-in functionality such as custom post types and custom fields that others won’t match.

The best path forward is to make a copy of your site, either locally or as a staging site on your server. Then you can switch themes, see what happens, and determine what if anything you may need to update within content or plugins to make sure you’re not losing anything important to your site.