foreach ( $submenu as $key => $item )
{
    echo $key[$item][0];
}

from print_r($submenu):

Array
(
    [index.php] => Array
        (
            [0] => Array
                (
                    [0] => Home
                    [1] => read
                    [2] => index.php
                )

            [10] => Array
                (
                    [0] => Updates <span class='update-plugins count-0' title=''><span class='update-count'>0</span></span>
                    [1] => update_core
                    [2] => update-core.php
                )

            [11] => Array
                (
                    [0] => Akismet Stats
                    [1] => manage_options
                    [2] => akismet-stats-display
                    [3] => Akismet Stats
                )

            [12] => Array
                (
                    [0] => Analytics360°
                    [1] => manage_options
                    [2] => analytics360.php
                    [3] => Dashboard
                )

            [13] => Array
                (
                    [0] => User searches
                    [1] => edit_pages
                    [2] => relevanssi-premium/relevanssi.php
                    [3] => User searches
                )

        )
)

Trying to access $submenu['index.php'][0]