<?php
//your array containing the items.
$aArray = array(
    array('Name' => 'Apple', 'Count' => 10),
    array('Name' => 'Tomato', 'Count' => 23),
    array('Name' => 'Tree', 'Count' => 4),
    array('Name' => 'Potato', 'Count' => 44),
    array('Name' => 'Apple', 'Count' => 73)
);

//the character or string you want to search.   
$startWithChar = 'A';

//get all items of the array starting with the specified character or string.  
$newArray = array_filter($aArray, function($v) use ($startWithChar) {
    return strpos($v['Name'], $startWithChar) === 0;
});

echo count($newArray); //2