Aside from proving you completed your year, what is the purpose of these? Do they have much of a role in terms of your time at the next place (anesthesiology) of residency?
Depends why you are asking for one in the first place. A letter stating you completed an intern year will not be of much use for gaining acceptance into an anesthesiology position.
They don't prove you finished the year. You need a certificate for that along with the PD's almighty signature.