getting error when i update image in my admin panel

I want to update my product table but when i update my product table,this error comes ErrorException in CreatesController.php line 201: Undefined variable: name

201 line is this: 'image'=> $name,

My product table contains following fields.

productname,image,price,category_id

//This is CreatesController

public function productupdate(Request $request, $id){

$this->validate($request, [

'productname'=>'required',

'image'=>'image|mimes:jpg,png,jpeg|max:10000',

'price'=>'required',

'category_id'=>'required'

]);

if($request->hasfile('image'))

{

  $file=$request->file('image');

  $new_name = rand(). '.' .

  $path=public_path().'/images';

  $name=$file->getClientOriginalName();

  $file->move($path, $name);

  $data=$name;

}

$data=array(

'productname'=> $request->input('productname'),

'image'=> $name,

'price'=> $request->input('price'),

'category_id'=> $request->input('category_id')

);

Product::where('id', $id)

->update($data);

return redirect('/item')->with('info','Product updated successfuly!');

}

via Chebli Mohamed