For example the person that starts the trade is the initiator of the trade, so what is the other person known as? Is there a word like initiator for the opposite party?
The other party that participates in a financial transaction. Every transaction must have a counterparty in order for the transaction to go through. More specifically, every buyer of an asset must be paired up with a seller that is willing to sell and vice versa.
Literally means the "opposite party."
Surely it must be responder.
This shows up in some search results, e.g.