I'm curious as to whether there exists a deontological system of morality where duties can be satisfied by providing the person to whom a duty is owed with something else that provides them with an equivalent amount of utility. The difference between this system and utilitarianism is that utilitarianism allows you to tradeoff utility across people, instead of just for a particular person. Is there a name for such a system of morality?
Kant actually has such a feature in his moral system: it's called imperfect duty.
Kant specifies two: Your Own improvement and Helping Others.
In both cases, the means of fulfillment are not specified but that you have a duty to help others is specified. Similarly, you as a rational being in need of the developed aid of others have an obligation to improve your abilities. But this does not decided which abilities you must improve.
There may be one inadequacy to what you are looking for insofar as the obligation is not attached to a specific person.
In moral theory, I would guess the closest we come to what you are describing would be promises with implicit alternate fulfillment conditions. E.g.,
I promised I would bring apples but I brought pears instead.
Depending on the conditions surrounding the promise, this would count as fulfillment because my obligation was to bring a healthy snack -- not specifically apples which served as a stand-in.
The same sort of thing also happens in second-order rights talk.