I've renamed a few CPTs slugs, for example Campaign (campaign) had to become Campaña (campana). It turned out that Toolset treats the slugs as the unique identifier and changing them practically breaks a lot of things.
Solution:
Toolset Types plugin is using WP function register_post_type() to create new post types, and treats the post type slugs as the unique identifier of each post type,
And the Repeatable Field Groups is based on one-to-many relationship, so each "Repeatable Field Groups" is also a custom post type, which is also use the post type slugs as the unique identifier.
In your case, it is not recommended to change the post type slug, but you can change the other post type settings, for example:
