Here is a list of Cooley's with given names as you noted, along with other Cooley's who served in the same companies.

It's usually a good bet that men from the same company were kin.

George Martin

John E. Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"K" Co. MS 37th Infantry

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Middleton Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"F" Co. MS 2nd State Troops Infantry

William Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"F" Co. MS 2nd State Troops Infantry

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Berry Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"C" Co. MS 7th Battn Infantry

L B. Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"C" Co. MS 7th Battn Infantry

Martin V. Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"C" Co. MS 7th Battn Infantry

Moses Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"C" Co. MS 7th Battn Infantry

Nelson Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
He was listed as:
* POW (date and place not stated)
"C" Co. MS 7th Battn Infantry
died disease POW, Camp Morton, IN
Buried: Crown Hill National Cemetery, Indianapolis, IN

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Harbert Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"F" Co. MS 8th Infantry

William Cooley

Residence was not listed;
Enlisted as a Private (date unknown).
"F" Co. MS 8th Infantry