Ellen,
I do not think there is a written policy, however practice has been to follow the name as used by Find A Grave, unless a better source shows that Find A Grave is in error. (As an example, the cemetery association secretary, she had been doing the job for 40 years, told me that the name at Find A Grave was wrong for one cemetery name that I worked on.)
In this case it would seem that Category: Elmwood Cemetery, Bethlehem Center, New York would be preferred.
Note that the category page is not set up properly, it should be a sub cat of Bethlehem Center. Bethlehem Center is identified as a hamlet in the northeast part of the town of Bethlehem at Wikipedia - the article on Bethlehem. So Bethlehem Center should be a sub cat of Bethlehem.