私に問題を引き起こしている行は ""Sheets(CStr(WS_M.Cells(n, START_C))).Cells(n, START_C).Paste"" です
これは、列3でタブ名を見つけてそのタブに移動し、そのタブにタブ名を貼り付けることになっています。
Const START_C = 3
Const MAX_TRAN = 1000
Const START_R = 2
Const MASTER = "MASTER"
Sub MOVEDATACORRECTLY()
Dim WS_M As Worksheet
Dim thisWB As Workbook
Set thisWB = ActiveWorkbook
Set WS_M = Worksheets(MASTER)
For M = START_R To (START_R + MAX_TRAN)
If WS_M.Cells(M, (START_C + 1)) = "" Then Exit For
Next M
M = M - 1
For n = START_R To M
WS_M.Cells(n, START_C).Copy
Sheets(CStr(WS_M.Cells(n, START_C))).Cells(n, START_C).Paste
Next n
End Sub