Suggestion list won't be displayed - php

Question

Let's say it looks like this:
<input type='text' name='customer' onkeyup='searchFor(this.value);' list='customers'>
And I have a datalist (which is embedded in PHP code which will be returned somewhere on the page)
<datalist id='customers'>
<option>$customer[0]['name']</option>
</datalist>
I want to enter a customer id and then it should return the name of the customer as a suggestion list below my text field.
That's my MySQL Query which works (var_dump() returns the correct value if entered a number)
$customer = $database->query("SELECT * FROM customers WHERE customerID LIKE ('%".$_POST["searchterm"]."%')")->fetchAll(PDO::FETCH_ASSOC);
But it doesn't show a suggestion list with my names.
In my opinion it's not working because I enter a number.
edited:
function searchFor(suchbegriff){
var xmlHttp = null;
if (typeof XMLHttpRequest != 'undefined') {
xmlHttp = new XMLHttpRequest();
}
if (!xmlHttp) {
try {
xmlHttp = new ActiveXObject("Msxml2.XMLHTTP");
} catch(e) {
try {
xmlHttp = new ActiveXObject("Microsoft.XMLHTTP");
} catch(e) {
xmlHttp = null;
}
}
}
if (xmlHttp) {
var url = "includes/search/search.php";
var params = "suchbegriff="+suchbegriff;
xmlHttp.open("POST", url, true);
xmlHttp.setRequestHeader("Content-type", "application/x-www-form-urlencoded");
xmlHttp.setRequestHeader("Content-length", params.length);
xmlHttp.setRequestHeader("Connection", "close");
xmlHttp.onreadystatechange = function () {
if (xmlHttp.readyState == 4) {
document.getElementById("ergebnis").innerHTML = xmlHttp.responseText;
}
};
xmlHttp.send(params);
}
}
edited2
search.php
<?php
include_once("../Dbo.class.inc");
if (isset($_POST["searchterm"])){
$customer = $database->query("SELECT * FROM customers WHERE customerID LIKE ('%".$_POST["searchterm"]."%')")->fetchAll(PDO::FETCH_ASSOC);
echo "<datalist id='customers'>";
foreach($customer as $key => $value){
foreach($value as $key2 => $value2){
if($key2 == "Name" || $key2 == "name"){
echo "<option>" . $value2 . "</option>";
}
}
}
echo "</datalist>";
} ?>