An order is placed by one and taken by another. It seems appreciate to call a person who takes an order a "order taker", but I don't know how to refer to the one who place an order.
Possible choices:
Either a word or a phrase is OK.
First, the word orderer is ok, if you really need that. But it's not very common.
Now in what situation? In a restaurant, you'd really just say "customer" or "patron". For some kind of supplies company, over the phone, I'd say "customer".
The most natural thing, if you must use the word "order", is "person who placed the order". That's what I would say.
'order-giver' is a valid and not too uncommon construct, and is quite general. (33million google results, compared with 539k results for orderer)
It does have a connotation of someone who has the authority to give orders, whereas, e.g. a customer in a restaurant is generally making more of a request, and has no formal authority over the person receiving the order.
Generally, a phrase such as the 'person who places the order' is more usual.
As my previous answer was deemed unsuitable, I’ll paraphrase it: For some time now, I have been using “order placer” to translate the Spanish phrase “quién hace el pedido” (person who places the order) into English in software strings. “Orderer” is another option, but as our colleague notes above, it doesn’t seem to be very widely used. Many people will just say “buyer/customer/client”, but the person or entity purchasing the commodity or service in question may not actually be the person or entity that places the order, which may be done an intermediary or agent of some sort. Hence, sometimes it is necessary to specify exactly who placed the order.
