Magento: get translated String in php - php

Question

Is it somehow possible to get the translated name of a category in Magento inside the php code? I.e. something like $category->getTranslatedName?
Background: I want to sort categories alphabetically, but having different names in different languages this only really works in the english shopview. My code:
foreach ($children as $child) {
$_children[$i]["child"] = $child;
$_children[$i]["name"] = $child->getName();
//gets english name, not the translated
$i++;
}
if (!function_exists('compare')) {
function compare($a,$b) {
return strcmp($a["name"],$b["name"]);
}
}
usort($_children, "compare");
for ($i=0; $i<count($_children); $i++) {
//code for main menu here
}
Edit: here is the part where it loads $children (it is taken from renderer.phtml):
$children = $menuTree->getChildren();
$parentLevel = $menuTree->getLevel();
$childLevel = is_null($parentLevel) ? 0 : $parentLevel + 1;
$counter = 1;
$childrenCount = $children->count();
$parentPositionClass = $menuTree->getPositionClass();
$itemPositionClassPrefix = $parentPositionClass ? $parentPositionClass . '-' : 'nav-';
$i = 0;
foreach ($children as $child) {
$_children[$i]["child"] = $child;
$_children[$i]["name"] = $child->getName();
$i++;
}
if (!function_exists('compare')) {
function compare($a,$b) {
return strcmp($a["name"],$b["name"]);
}
}
usort($_children, "compare");
for ($i=0; $i<count($_children); $i++) {
//Code for main menu
}