Generate the post title from ACF fields

The $post_id value get in save_post hook might be revision ID. So to retrieve real post ID, you can use this function wp_is_post_revision()

Try to change your code as follows,

function set_post_title_from_acf($post_id) {
    
    // If this is a revision, get real post ID
    if ( $parent_id = wp_is_post_revision( $post_id ) ) 
        $post_id = $parent_id;

    $my_post = array();
    $my_post['ID'] = $post_id;

    if (get_post_type($post_id) == 'staff') {

        $first_name = get_field('first_name', $post_id);
        $last_name = get_field('last_name', $post_id);

        $my_title = $first_name . ' ' . $last_name;
        $my_post['post_title'] = $my_title;
        $my_slug = sanitize_title($my_title);
        $my_post['post_name'] = $my_slug;
        
        // unhook this function so it doesn't loop infinitely
        remove_action( 'save_post', 'set_post_title_from_acf' );
        
        wp_update_post($my_post);
        
        // re-hook this function
        add_action( 'save_post', 'set_post_title_from_acf' );
        
        
    }
}

add_action('save_post', 'set_post_title_from_acf');

Nb: If we are calling wp_update_post() inside save_post hook, it will create an infinite loop. To avoid this, unhook the function before calling the function and then re-hook it as in the above code.