single-word-requestsword-choice
Andrew wants to make an appointment with Sally but Sally needs to determine
whether the time Andrew stated is suitable for her.
What do you call Andrew and Sally? I found words like appointee, appointer, subject but they all don't seem to fit.
I think Sally may be called object but I'm not sure about Andrew.
A key, or a token, depending on the context.
With the word key, I was referring to part of a machine component that is specially shaped to slot into, and lock with, the keyway of a shaft.
(Though, of course, a key more commonly refers to an object that slides in through the keyhole of a lock, and acts to unlock it.)
A token would be something similar to a coin, which would pass straight though a slot.
I think perhaps the term cosy is appropriate. A quick Google search reveals a number of items similar to your picture which are being marketed as a "phone cosy"
For example, a red knit Phone Cosy.
Another application of the term cosy is a tea cosy
Seems to me you might be looking at a ball cosy, although it is more of a neologism than a defined word.
Best Answer
I would try the general terms inviter and invitee, or requester and invitee.
I wouldn't use appointer and appointee, as these terms refer to the appointment of positions (like Cabinet Secretaries and such). Your question seems more concerned with the setting of meetings.