No, functionality will not be damaged just look and fill will change as per your new theme.
Thanks & Regards,
I don’t mean changing the theme, but changing the theme name, does it break the functionality of WordPress or the theme?
Not really. When WP cannot find its normal theme because its name was changed, it’ll use one of the default twenty* themes. Just re-activate your theme under its new name. You will likely need to re-specify customizer options and maybe even other elements like widgets, but nothing will “break” per se.
If you change a theme name that came from the WP repository, it will no longer be updated, which could allow security issues to become revealed over time. In such cases, you’re better off creating a child theme with the desired name.