Two 1945 newspapers confirming the name as Priesley Paul Cooper, Jr, including one supposedly written at his father's request to announce his death, so we can presume the name is correct:
https://www.newspapers.com/newspage/44866823/
https://www.newspapers.com/newspage/44915961/
As for having no MACR, there is a grey zone about USAAF losses during WWII. There are two sets of available reports:
_ MACR were written only when at least one crew was posted missing (and if the loss was overseas).
_ accident reports covered all crashes occuring in friendly area and not related to eney activity: training crashes in USA are for example included (including some cases of missing crew) but also many crashes from aircraft operating from bases in Europe and crashing before reaching the enemy area or on return of a mission, but without enemy action (like a crash due to fog or to a landing mishap). But for aircraft involved in operations there is no absolute rule: one may have an accident report and one not, even if loss circumstances are the same.
But there is one case that will not be covered by the above reports: US aircraft lost in operations and crashing in friendly area. These will usually be only covered in the unit war diary, and if a crew was killed, in his individual IPDF file.
So in your case, this last file should exist for Priesley Paul Cooper and will help to know how and where he died.
Edited: if you don't have it, the book "Spitfires and Yellow Tail Mustangs" (history of 52nd FG) has nothing about Cooper than it being killed by Flak, with no area or aircraft given and a wrong first name.