There are 35 cards in the file indexed as:
Brown, Joseph William (24)

Cards:

1 Index Card Joseph William Brown, 1st. Co. D, F & S, 8th Virginia Cavalry, Private Ord. Sgt.

2 Pvt. Joseph William Brown, age 24, Capt. Wm. Henderson French’s Co.,
Virginia Volunteers* Joined and enrolled July 31, 1861 at Jno, Neely’s
by Col. Jno. S. Carr for 12 months, present at muster-in September 20,
1861 at Princeton, Mercer County * The company subsequently
became (1st) Company D, 8th Regiment Virginia Cavalry

Note, there are no further cards for this Pvt. Brown

3 J. W. Brown, O. Serg, 8th Regiment Virginia Cavalry, recorded present
F & S Muster for Mar/Apr, 1863, last paid December 31, 1862, enlisted
June 25, 1861 at Falls Kanawha by J. C. Rigg for 3 years

With one exception, the remainder of the cards in this record are for J. W. Brown,* Ordnance Sergeant

* Initials only, full name not spelled

9 J. M. Brown, Pvt. Co. G. 8th Va., Receipt Roll for clothing for 4th Qr.,
1864, issued Nov 17th, 1864, /s/ John N. Brown, paroled prisoner

This is John N. Brown, Pvt., Co. G, captured at Loudoun Co., Va. July 14, 1864, age 22 in 1865

M324: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Virginia

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In the Miscellaneous file, there is a file for a Jos. W. Brown, Card No. 1 is a Reference Card, which displays:
See Manuscript No. 1396 Page ______
For burial
Note, no idea to who this record refers

Card No. 2 is a Receipt Roll for pay, May, 1864, Occupation Boatman
/s/ Joseph W. Brown, Smithville, N. C.
Note, would believe these two cards represent different individuals.

M347: Unfiled Papers and Slips Belonging in Confederate Compiled Service Records

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I am not aware of any procedure on how these records may be corrected.

Suggest you contact the Old Army Archivists at the National Archives in Washington, D. C.