I know, I am answering this question very late but I am posting an answer for this just in case anyone else is looking out for the answer.
Please create a child theme and in that child theme create file /woocommerce/my-account/my-downloads.php. Add following content in that file
<?php
/**
 * My Orders
 *
 * Shows recent orders on the account page
 *
 * @author      WooThemes
 * @package     WooCommerce/Templates
 * @version     2.0.0
 */
if ( !defined( 'ABSPATH' ) ) {
    exit;
}
function wdm_print_download_file_name( $download, $product_meta ) {
    if ( is_numeric( $download['downloads_remaining'] ) )
        echo apply_filters( 'woocommerce_available_download_count', '<span class="count">' . sprintf( _n( '%s download remaining', '%s downloads remaining', $download['downloads_remaining'], 'woocommerce' ), $download['downloads_remaining'] ) . '</span> ', $download );
    echo apply_filters( 'woocommerce_available_download_link', '<a href="' . esc_url( $download['download_url'] ) . '">' . $product_meta[$download['download_id']]['name'] . '</a>', $download ); //Print file name
}
if ( $downloads = WC()->customer->get_downloadable_products() ) :
    ?>
    <h2><?php echo apply_filters( 'woocommerce_my_account_my_downloads_title', __( 'Available downloads', 'woocommerce' ) ); ?></h2>
    <ul class="digital-downloads">
        <?php
        $all_product_ids = array();
        $all_download_ids = array();
        $download_ids_used_till_now = array();
        foreach ( $downloads as $download ) :
            ?>
            <?php
            do_action( 'woocommerce_available_download_start', $download );
            if ( !in_array( $download['product_id'], $all_product_ids ) ) { //Check if current product id is already there in $all_product_ids array. If it goes in this loop, that means it is new product id
                $product_meta = get_post_meta( $download['product_id'], '_downloadable_files', true ); //All download ids of the product
                $all_product_ids[] = $download['product_id']; //Push Current download's Product id to an array
                $all_download_ids = array_keys( $product_meta ); //Get all download ids of the current product
                echo '<li><span>' . get_the_title( $download['product_id'] ) . '</span><ul>'; //Print product name
                $download_ids_used_till_now[] = $download['download_id']; //add download id to an array
                echo '<li>';
                wdm_print_download_file_name( $download, $product_meta );
                echo '</li>';
                $check_if_this_is_last_element = array_values( array_diff( $all_download_ids, $download_ids_used_till_now ) );
                if ( empty( $check_if_this_is_last_element ) ) { //This is last download id of a product
                    echo '</ul></li>'; //close ul and li tags
                }
            } else { //product id is already in use.
                $check_if_this_is_last_element = array_values( array_diff( $all_download_ids, $download_ids_used_till_now ) );
                if ( isset( $check_if_this_is_last_element[0] ) && $download['download_id'] == $check_if_this_is_last_element[0] ) { //This is last download id of a product
                    echo '<li>';
                    wdm_print_download_file_name( $download, $product_meta );
                    echo '</li>';
                    echo '</ul></li>'; //close ul and li tags
                    unset( $download_ids_used_till_now );
                    unset( $all_download_ids );
                } else { //There are few more download ids
                    $download_ids_used_till_now[] = $download['download_id'];
                    echo '<li>';
                    wdm_print_download_file_name( $download, $product_meta );
                    echo '</li>';
                }
            }
            do_action( 'woocommerce_available_download_end', $download );
            ?>
        <?php endforeach; ?>
    </ul>
    <?php endif; ?>
Above code is tested with WooCommerce 2.1.12.