First remove action of customizer then add your action with new function name.
in your child-theme functions.php
add_action( 'init', 'remove_my_action');
function remove_my_action() {
remove_action('customize_register', 'business_prime_settings_control',10);
}
require_once dirname( __FILE__ ) . '/inc/business-prime-customizer.php';
in your child-theme/inc/business-prime-customizer.php
change name of function and callback
function business_prime_settings_control_child($wp_customize) {
# here your all customizer settings code
}
add_action('customize_register', 'business_prime_settings_control_child');
Remove other extra actions and declared functions. otherwise you will get : Cannot redeclare Fatal error.