If you want to get the first item, you can use the first method.
{{ $new_product->images->first()->image_name }}
You also have the offsetGet method to get an item at a given offset.
{{ $new_product->images->offsetGet(0)->image_name }}
You can also loop through the collection though and do this:
@foreach ($new_product->images as $image)
{{ $image->image_name }}
@endforeach
Note: The first two method will only work if your products have images. If they don't, then Laravel will return an empty collection. The third method of looping through the collection will work in all cases.
If you want to make sure that products have images, you can use the has method.
$new_products = Product::with('images')->has('images')->orderBy('created_at', 'desc')->take(10)->get();
This will only return products that have at least one image.
Docs on collection methods: http://laravel.com/docs/master/collections#method-first
Docs on relationships: http://laravel.com/docs/5.1/eloquent-relationships