Grosh uses the list of users the list is shared with as a picklist for the From / To fields. So head over to Menu->Sharing and add the emails of the users that the list involves. After the users are active in the system, their name will appear in the pick lists where you simply select them.
Note: you should not specify the recipient (To) person until the wish has been entered with all details, as this locks the field for the recipient. After being locked, the wish cannot be altered and at the same time, it's a signal to buyers (From persons) that this wish is now ready and can be assigned to a person.
A person wanting to buy a gift can simply look through the wishes and then open an item and assign himself/herself under From. This will indicate to others that the person has taken responsibility of buying the gift.