For another reference, a second document, "U.S., Registers of Deaths of Volunteers, 1861-1865," indicates another name for the hospital, Div F.H, 2" A. C. It is referenced as "field hospital at Munson's Hill" in a roster list for the 59th NY Infantry.
A soldier who did not survive after being treated there is buried at Arlington National Cemetery. I have seen reference to some field hospitals, but didn't know if this one is referred to as another name.
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We searched the National Archives Catalog and located a series titled Registers of Deceased Volunteer Soldiers, 1861-1864 in the Records of the Adjutant General’s Office, 1762 - 1917 (Record Group 94) that may contain information about soldiers of the 59th New York Infantry Regiment who died in a field hospital near Munson’s Hill. We also located the Regimental and Company Books of Civil War Volunteer Union Organizations, 1861 - 1867 in Record Group 94 that includes Regimental and Company Books of the 59th New York Infantry Regiment with Morning Reports for Companies A - K. The reports may indicate which soldiers of the 59th were at various hospitals. For information about these records, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
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You may wish to review these websites: Arlington National Cemetery--Civil War Era; Battle Unit Details - The Civil War (US National Park Service); 59th NY Infantry Regiment during the Civil War; Civil War in the East 59th New York Volunteer Infantry Regiment; and 59th Regiment, New York Infantry for additional information and/or resources.
We hope this is helpful. Best of luck with your research!