Anyone can be requested to give feedback. This feedback can be for the requester himself or someone else. There are two ways to respond to feedback requests, let us both options.
Link within email notification of feedback request
When someone asks for feedback from you, you will be notified via email, that email will contain a direct link to responses tab of 'my feedback' page. Clicking on this link directs you to my feedback page and it will also open respond feedback pop up to respond to the request.
Requests & responses tab on my feedback page
Same request will be available on my feedback page >> requests tab. You can click on respond option at right side of request message to respond the same feedback request.
One cannot change 'receiver' of the feedback or 'associated Jira issue' while giving the feedback. While responding you only have control over who is it shared with, feedback tag, labels & the message.