I don’t think I would bother giving a one-year-old privacy, but by age two or three I would (if it is safe to do so in this situation and if he or she is able to feel and express embarrassment).
If (on the other hand) the child is not able to experience embarrassment yet (or if close supervision is required in this situation, for safety reasons) then I would probably watch him or her and do a change once he or she is finished.