Attached is the research I did while working on a mod. It's an Excel spreadsheet but you can open it with something like Open Office. Many of the fields won't matter to you, but I included the first/last name (and middle initial/name if necessary), the year of birth, dates of rank and appointment for brigadier/major/full general (and colonel when available). It's separated into CSA and Union sheets, and further subdivided for state militia appointments and the few Union generals who had 3-month appointments at the start of the conflict.
As you probably know, some of the personalities represented in the game were only brevetted general towards the very end of the conflict, and some of them were never general officers at all. I believe the game contains some dupes, and I can only guess as to why. I suspect some of it is because the models were carried over from the previous version of AACW.
C. Field: Charles W. Field.
https://en.wikipedia.org/wiki/Charles_W._Field
O. Wilcox: Probably Orlando Willcox.
https://en.wikipedia.org/wiki/Orlando_B._Willcox
R. Mitchell: Robert B. Mitchell, another dupe.
https://en.wikipedia.org/wiki/Robert_Byington_Mitchell
A. Williams: Alpheus Williams.
https://en.wikipedia.org/wiki/Alpheus_S._Williams
E. Weer: I think this is William Weer, didn't find any other Weer that came close.
https://en.wikipedia.org/wiki/William_Weer
S. Jackson: your guess is as good as mine.