If you can provide any additional names of men from these regiments, please respond to this thread.
From Rowland, Dunbar; "Military History of Mississippi, 1803-1898", it appears the 36th Mississippi Infantry (Hebert's Brigade) had only "1 killed" in action. Name currently unknown.
Also according to Rowland, the 37th Mississippi Infantry (Hebert's Brigade) had "5 killed." Currently, only one, Private S.V. (Sylvester) Simmons, Co H has been confirmed as KIA by service record. The other 4 (others?) remain unidentified.
Again, Rowland states among the 38th Mississippi Infantry (Hebert's Brigade), there were "4 killed." None of these, as yet, has been identified.
As for the 40th Mississippi Infantry, "Battles and Leaders of the Civil War," Yoseloff ed., pg 736, there is a report of "10 killed" within this regiment (part of Martin's Brigade). To date, in reviewing the service records of the regiment, there are 12 confirmed casualties of this regiment who've been identified who'd likely been buried at Shady Grove. These are:
Capt. R.C. Coleman, Co H, 40th MS - KIA 19 Sept 1862 Iuka
Pvt. W.L. Wheeler, Co B, 40th MS - KIA 19 Sept 1862 Iuka
?? Pvt. D.L. McKay, Co C, 40th MS - POW "died of disease" (noted as captured 19 Sept 1862, but at "Corinth")
Cpl. Samuel McKay, Co C, 40th MS - KIA 19 Sept 1862 Iuka
Pvt. W.P. Strahan, Co D, 40th MS - (William Preston Strahan) - KIA 19 Sept 1862 Iuka
Pvt. Henry W. Webb, Co F, 40th MS - WIA 19 Sept 1862 Iuka and Died of Wounds at Iuka 26 Sept 1862
Pvt. Henry W. Holland, Co F, 40th MS - KIA 19 Sept 1862 Iuka
Pvt. S.M. Ware, Co G, 40th MS - "Died from wounds in fight at Iuka" no date of death indicated
Pvt. J.T. Smith, Co I, 40th MS - POW Iuka "died in hands of enemy" 30 Sept 1862 at Iuka
Pvt. W.W. Barnes, Co K, 40th MS - KIA 19 Sept 1862 Iuka
Pvt. Abner Mays, Co K, 40th MS - KIA 19 Sept 1862 Iuka
Cpl. Jesse Mays, Co K, 40th MS - KIA 19 Sept 1862 Iuka