I've been experimenting with tasks because of your question and I haven't
found any particular use for the "Requested By" field, since it doesn't
display on a Task form, as far as I can tell, only when displaying a table
view of the Tasks folder and only when you add it to the view with Field
Chooser.  I don't see any way to populate that field when creating a new
task or assigning a task to a person.  I tried sending a "Task Request" to
my home address because I figured that Outlook might fill the field in with
the sender information, but it didn't.  However, I tried it within an
Exchange domain where both sender and recipient were on the same Exchange
server and then it was filled in with the sender of the task.  So,
apparently Exchange is required or I didn't send it correctly to my home
address.

All that said, if you display it in the view, you can enter information
there if you enable in-cell editing.  While viewing your Tasks folder in a
table view (like Simple List), right-click an empty area of the view and
choose Other Settings.  Check the box labeled "Allow in-cell editing", then
click OK.  You should then be able to put what you'd like in the Requested
By field.