Register form how to get Total Control of it

Copy this function and modify it as per your needs. 

function custom_register_new_user( $user_login, $user_email ) {
    $errors = new WP_Error();

    $sanitized_user_login = sanitize_user( $user_login );
    $user_email = apply_filters( 'user_registration_email', $user_email );

    // Check the username
    if ( $sanitized_user_login == '' ) {
        $errors->add( 'empty_username', __( '<strong>ERROR</strong>: Please enter a username.' ) );
    } elseif ( ! validate_username( $user_login ) ) {
        $errors->add( 'invalid_username', __( '<strong>ERROR</strong>: This username is invalid because it uses illegal characters. Please enter a valid username.' ) );
        $sanitized_user_login = '';
    } elseif ( username_exists( $sanitized_user_login ) ) {
        $errors->add( 'username_exists', __( '<strong>ERROR</strong>: This username is already registered. Please choose another one.' ) );
    }

    // Check the e-mail address
    if ( $user_email == '' ) {
        $errors->add( 'empty_email', __( '<strong>ERROR</strong>: Please type your e-mail address.' ) );
    } elseif ( ! is_email( $user_email ) ) {
        $errors->add( 'invalid_email', __( '<strong>ERROR</strong>: The email address isn&#8217;t correct.' ) );
        $user_email="";
    } elseif ( email_exists( $user_email ) ) {
        $errors->add( 'email_exists', __( '<strong>ERROR</strong>: This email is already registered, please choose another one.' ) );
    }

    do_action( 'register_post', $sanitized_user_login, $user_email, $errors );

    $errors = apply_filters( 'registration_errors', $errors, $sanitized_user_login, $user_email );

    if ( $errors->get_error_code() )
        return $errors;

    $user_pass = wp_generate_password( 12, false);
    $user_id = wp_create_user( $sanitized_user_login, $user_pass, $user_email );
    if ( ! $user_id ) {
        $errors->add( 'registerfail', sprintf( __( '<strong>ERROR</strong>: Couldn&#8217;t register you... please contact the <a href="https://wordpress.stackexchange.com/questions/87421/mailto:%s">webmaster</a> !' ), get_option( 'admin_email' ) ) );
        return $errors;
    }

    update_user_option( $user_id, 'default_password_nag', true, true ); //Set up the Password change nag.

    wp_new_user_notification( $user_id, $user_pass );

    return $user_id;
}

Read this page to display your own error messages.

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Front-end Register Form

How to display WordPress User Registration Form in front end of the website?

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