The front of the monument shows signs that a plaque was once attached there, though it is unclear (by me) what was inscribed upon it. Being the same size as the one attached on the back of the monument - did it become dislodged from the front, and was then reattached on the opposite side? 

CO. E, 4TH N.H.V.
KILLED OR DIED IN CIVIL WAR

Lieut. Frank B. Hutchinson
Born Oct. 17, 1837 - killed May 16, 1864
grave unknown

Sergt. Williard K. Cobb
Born Dec. 26, 1843
Killed Sep. 29, 1864
grave unknown

Amos Cressy
Born Oct. 5, 1822
Died of wounds June 6, 1864
​grave unknown

Below are older photos, taken in 2013, before tree was removed

Memorial Park on Chester Road in Auburn, New Hampshire. Plaque on front gives a 1976 date for the memorial. Tablets on the north and west side honor the World War II and Korean/Vietnam War veterans (World War I is a separate memorial on a nearby boulder), while the south face holds a plaque for the Civil War Soldiers from Auburn.

Below are the 49 names listed on the above memorial plaque, with their regiments (when known) added below their names. 

Note: There are several men whose service records still need verifying. There were also several soldiers who were Auburn men that were somehow left off this tablet, including:
Sylvester E. Emery, 8th NH; Luther and Henry M. Preston, 1st NH HA

Burial places, as they are found, will be recorded in the following "virtual cemetery" on Find a Grave: Civil War Soldiers of Auburn, NH

GPS: 43.001647, -71.346300
Opposite the town hall at 47 Chester Rd, Auburn, NH
Photos taken 5 June 2021 by S. Dow

OUR FALLEN HEROES 1861-'5

Located on the grounds of the Lempster Historical Society at 10 2nd NH Turnpike. GPS:  43.225872, -72.178232
​
Visited today, 08 August 2020, following a parade held in town during the 121st Lempster Old Home Day Celebration. Soldier's data added from Ayling's Revised Register and NH Service Records - S.Dow

In Pittsfield, New Hampshire's Floral Park Cemetery, there is a memorial stone, engraved with the names of the soldiers from this town who never returned home from the Civil War. It was erected by the Capt Asa W. Bartlett Camp, No. 39, Sons of Veterans.

Using Ayling's Revised Register and the History of Pittsfield, I've added the soldier's unit and cause of death to their memorial.

IN HONORED MEMORY OF

George W. Berry - Co. K, 13th NH; wd 6/15/64, Petersburg, VA; died of wnds 6/16/64
John Brooks - Co. H, 3rd NH; wd 6/16/64 Ware Bottom Church, VA; d. 6/17/64, Bermuda Hundred
Henry Plummer Brooks - Co. H, 3rd NH; died of dis, 4/14/65 Wilmington, NC 
William Campbell - Co. G, 7th NH; KIA 7/18/1863, Fort Wagner, SC
John Cate - Co. G, 15th NH; wd 5/27/63, Port Hudson, LA; d. wnds 6/8/63, Baton Rouge
Joseph M. Chesley - Co. E, 2nd NH; KIA Gettysburg, 7/2 or 7/3
Willard K. Cobb - Co. E, 4th NH; KIA 9/29/64, New Market Heights, VA
George W. Davis - Co. E, 4th NH; a POW, d. after being paroled in Annapolis, MD
Joseph C. Dennett - Co E., 4th NH; d. of sickness, Hilton Head, Jan '64
Justice C. Drake - Co. B, 1st NH Cavl d. 8/14/64, Andersonville Prison
John J. Drake - Co. D, 11th NH; d. of dis. 11/10/64
Israel Drew - Co. G, 8th NH; died Camp Parapet, LA, 8/23/62
John S. Eaton - Co. E, 8th NH; disch for illness, died on voyage home, 11/2/62 and bur at sea
Lewis E. Edgerly - Co. G, 7th NH; missing at Fort Wagner, 7/18/63
Samuel R. Green - Co. A, 5th NH; wd at Gettysburg, 7/2/63, died 7/29/63

Edwin A. Kelley - Co. F, 12th NH; KIA Chancellorsville, 5/3/63
William T. Knight - Co. E, 2nd NH and Co. B, 12th NH; KIA 7/2/63 at Gettysburg 
Henry B. Leavitt - Co. G, 7th NH; wd at Fort Wagner; died after amputation of leg, 7/22/63, Charleston, SC
Jeremiah Marston - Co. F, 12th NH; wd/killed 6/3/64, Cold Harbor, VA
John C. Mason - Co. G, 15th NH; died 8/3/63 Sandusky, OH, on way home due to sickness
John B. Merrill - Co. F, 12th NH; KIA Chancellorsville, 5/3/63
George F. Meserve - Co. F, 12th NH; captured at Petersburg 5/16/64; died in Andersonville Prison
James D. Meserve - Co. B, 7th NH; killed at Fort Wagner, 7/18/63
George H. Reynolds - Co. F, 12th NH; KIA Chancellorsville, 5/3/63
Isaiah Swain - Co. G, 15th NH; sick on return home, died at Mound City, IL, 8/5/63
Daniel P. Tilton - Co. G, 7th NH; captured at Olustee, FL; died at Andersonville, 7/26/64
William H.H. Watson - 14th NH; died of fever 5/30/64, New Orleans
Hazen W. Willey - Co. G, 7th NH; wnd at Fort Wagner 7/18/63 and captured; died in Charleston, SC, 7/20 or 7/21
George Winkley - Co. F, 12th NH; died at Falmouth, VA, 5/24/63, of disease
​Enoch M. Young - Co. G, 15th NH; died at New Orleans, 6/2/63, from exhaustion/sickness

WHO ENLISTED FROM PITTSFIELD TO SERVE
THE UNION IN THE CIVIL WAR, BUT DID NOT
RETURN; WHOSE SAD PORTION WAS A SOLDIER'S
DEATH AND AN OBSCURE SOUTHERN GRAVE.

ERECTED BY
CAPT. ASA W. BARTLETT Camp No. 39, S. of V.

See:
History of Pittsfield, N.H. in the Great Rebellion on [Internet Archive], for excellent biographies of all the men who served from Pittsfield, including those engraved on the above memorial.
Notes:
The Sons of (Union) Veterans Camp No. 39 was named for Asa W. Bartlett, who was captain of Co. C, 12th NH Infantry (prev 2nd Lieut of Co. G, and 1st Lt of Co. K). He was author of the History of the Twelfth NH Regiment. Camp information, such as charter date, is not known at this time. 

The Civil War Soldiers Memorial in Pine Grove Cemetery, Salem, New Hampshire

This memorial (date of construction unknown) lists the names of 13 Civil War soldiers from the town of Salem, NH who died during the War. Their names, listed in order by regiments:

Aaron Goodwin Co. B 2nd NH Vols
Born in Haverhill, NH, a res of Salem when he enlisted for 3 months on 23 Apr 1861, age 20. Not mustered in, he reenlisted for 3 years on 15 May, and must in as private on 1 June '61. Wounded at Gettysburg on 2 July 1863, he died on 17 Aug at McDougall Gen. Hosp at Fort Schuyler, New York. He is buried in Cypress Hills National Cem.
Levi W Simons Co. H 4th NH Vols
Born in Alexandria, NH, a res of Salem when he enlisted on 2 Sept 1861, aged 35, and mustered in on the 18th as a corporal. He died on 2 Oct 1863, and is buried [as Simonds] in the National Cemetery in Beaufort, SC [grave #1516] note: Aylings shows he rec a disability disch on 24 Oct 1863 at Morris Island, SC, as does must-out papers.
Benjamin Day Foster Co. G 6th NH Vols
A Salem, NH native, he enlisted, at age 18, on 17 Oct 1861, and mustered in as a private on the 28th. He was killed in action on 29 Aug 1862.  
Isaiah Milton Kelly Co. G 6th NH Vols
​At age 37, the Salem native enlisted on 6 Nov 1861, and was mustered in as a private on 28 Nov. He was killed in action at Bull Run on 29 Aug 1862.
Charles E Bailey Co. B 7th NH Vols
Born in Salem, and a resident there when he enlisted on 14 Aug 1862, aged 23. Mustered in as a private on the 28th of Nov '61. Captured 18 Jul 1863 at Fort Wagner, he died of disease on 3 Jan 1864 in Richmond, VA (Confed Gen. Hosp). He is buried in Richmond National Cem. 
George Whidden Co. B 7th NH Vols
Records show him in Co. D, and was born in Londonderry, NH. Credited to Salem when he enlisted on 14 Aug 1862, aged 29, and mustered in on the 21st as private. Wounded 14 May '64 at Drewry's Bluff, VA, he died as a result of his injuries on 25 June at DeCamp Gen Hosp on Davids Island, New York. His body was returned home, and buried in Sunnyside Cem, Londonderry.
David Bartlett Co. C 7th NH Vols
Company shown as B in records, he was born in West Newbury, MA and a res of Salem when enl on 23 Sept 1861. Must in as pvt on 1 Nov '61, he re-upped on 27 Feb '64. He died from disease in Wilmington, NC on 3 June 1865.
Benjamin W. Cluff Co. D 8th NH Vols
A Salem native, and brother of Isaac below, he enlisted at age 25 on 30 Dec 1861, and must in the following day as a private. He died from typhoid at the St James General Hospital in New Orleans on 29 Dec 1862.
John Robinson Co. C 9th NH Vols
Born in Londonderry, he was in Salem when enlisted on 4 June 1862, aged 25, and must in on 22 July as pvt (later appointed corporal). Wounded at Fredericksburg on 13 Dec 1862, he died on 2 Jan '63 at Washington, DC.
John G. Bodwell Co. E 11th NH Vols
born/res: Salem; enlisted, age 20, on 15 Aug 1862. Must in 29 Aug as pvt. Died of typhoid on 28 Dec 1862, at the regimental hospital in Falmouth, VA.
Isaac N. Cluff Co. K 15th NH Vols
Brother to Benj'm (in the 8th NH), and Salem native, enlisted 11 Sept 1862 and must in as pvt on 16 Oct. He died of disease on 2 Aug 1863 in Memphis, TN.
Edward B. Mosher Co. K 15th NH Vols
Born in Temple, Maine, he was a res of Salem, aged 44, when enlisting on 8 Sept 1862. He was mustered in 16 Oct, a private, and served until being killed in action at Port Hudson, LA.
Henry Percy Co. K 15th NH Vols
This name not found in the rolls of the 15th NH, or in pension index.

​Notes: 
While attempting to find out who "Henry Percy" was, I noticed there was another Salem resident in Co K, 15th NH, who died while serving, and is not on this memorial. He was:
William F Mansfield
Born in Lynn, MA, and res of Salem when enlisted on 15 Sept 1862, aged 18. Must in as pvt on 16 Oct '62, he died from disease on 27 Mar 1863 in Carrollton, LA, from typhoid fever.

​Sources:
- Ayling's Revised Register
- U.S. Register of Deaths of Volunteers (on Ancestry)
- Muster out Rolls on Family Search (NH Service Records)
- Photo of memorial was taken on 28 May 2018, during a Memorial Day service held by members of the Gilman Sleeper Camp #60