Final answer:
The shared name of the only pair who weren't related among the five sets of presidents is Roosevelt.
Step-by-step explanation:
The shared name of the only pair of presidents who weren't related among the five sets is Roosevelt.
There were two sets of presidents with the last name Roosevelt:
- Theodore Roosevelt and Franklin D. Roosevelt
- Theodore Roosevelt and Franklin D. Roosevelt were fifth cousins, but they are not considered related for the purposes of this question.
Therefore, the shared name of the only pair who weren't related is Roosevelt.