How to change a specific admin label

You could try that with the gettext filter in the following manner.

function rename_header_to_logo( $translated, $original, $domain ) {

    $strings = array(
        'Header' => 'Logo',
        'Custom Header' => 'Custom Logo',
        'You can upload a custom header image to be shown at the top of your site instead of the default one. On the next screen you will be able to crop the image.' => 'You can upload a custom logo to be shown at the top of your site instead of the default one. On the next screen you will be able to crop the image.'
    );

    if ( isset( $strings[$original] ) && is_admin() ) {
        $translations = &get_translations_for_domain( $domain );
        $translated = $translations->translate( $strings[$original] );
    }

    return $translated;
}

add_filter( 'gettext', 'rename_header_to_logo', 10, 3 );

You might want to check that the text doesn’t conflict with another “header” text somewhere else.