<?php

$arr = array(array('name' => 'email', 'value' => 'teste@teste.com'),
             array('name' => 'code', 'value' => 'D9CI8C'),
             array('name' => 'nome', 'value' => 'fulano'),
             array('name' => 'problema', 'value' => 'algo errado')
);


$novo = array();
foreach($arr as $item) $novo[$item['name']] = $item['value'];

print_r($novo);