As answered here, .Name(p => p.Orders.First().Name)
is telling ES to map the field 'Name' on the Product document. Instead, you want to map to the 'Name' field on Orders, which is an array in your Product document.
Try this instead:
client.Map<Product>(m => m
.Properties(pp => pp
// Map Product.Name
.String(s => s
.Name(p => p.Name)
.IndexAnalyzer("normalize")
)
// Map Product.Orders.Name
.Object<List<Order>>(o => o
.Name(p => p.Orders)
.Properties(op => op
.String(s => s
.Name(os => os.First().Name)
.IndexAnalyzer("normalize"))))
));