Change case the data inside a column
For testing your code following assumption are made


Sub Entry_Point was disabling screen updating, events and display alerts.  
Sub Exit_Point was enabling screen updating, events and display alerts.
It is being used for importing data from multiple files and to be finally placed in SheetShMN one below another


according to the above assumption following modification was done

1 Sheet ShMN is being cleared with in loop For FileCnt = 1 To UBound(FiletoOpen) with line ShMN.Rows("2:" &amp; ShMN.Rows.Count).ClearContents. I pulled out the line out of the For loop for testing purpose.

2.The line  ShMN.Cells(2, c).PasteSpecial modifed to ShMN.Cells(lastRow, c).PasteSpecial for placing data from each file one below another (This to avoid 1st files data to be overwritten by subsequent files data).  


Finally as the cause of slow performance, it is found the Case Changing codes are placed inside header finding loop.So it is executing Number of files X Number of columns times. I pulled it out of even file loop and placed just after completion of Data import.
Myrange was defined "B2:B" &amp; Rows Count. I change it to Set MyRange = ShMN.Range("B2:B" &amp; ShMN.Cells(Rows.Count, 2).End(xlUp).Row)


For Testing purpose, I used 5 files consisting same Data of 500 rows X 52 Columns with header. I have not used Calculation mode manual, Screen update disable etc (as I generally don't prefer these). You may use the techniques as per your requirement. It takes around 50 seconds to import all 5 files data and only another 3 odd seconds to change the case of B column (in my old laptop)

My test code:

Option Explicit
Sub test()
Dim Tm As Long
Dim FiletoOpen As Variant, ShDataN As Worksheet, ShMN As Worksheet
Dim FileCnt As Long, SelectedBook As Workbook, MyRange As Range, cell As Range
Tm = Timer
Set ShDataN = ThisWorkbook.Sheets(1)
Set ShMN = ThisWorkbook.Sheets(2)



    Dim lastRow As Long, LastTemp As Long 'lasttemp is "last row for table template
    Const StartRowTemp As Byte = 1
    Dim c As Byte 'number of columns
    Dim GetHeader As Range   'find

    'Call Entry_Point 'to prevent screen updating and display alert, the value is False
    'Application.ScreenUpdating = False
    'Application.EnableEvents = False
    Application.DisplayAlerts = False
'    On Error GoTo Handle

    'pick files to import - allow multiselect
    FiletoOpen = Application.GetOpenFilename _
    (FileFilter:="Excel Files (*.xlsx), *.xlsx", Title:="Select Workbook to Import", MultiSelect:=True)

    If IsArray(FiletoOpen) Then
    'delete the content from Analysis table
    ShMN.Rows("2:" &amp; ShMN.Rows.Count).ClearContents   ' moved out of For foleCnt loop

        For FileCnt = 1 To UBound(FiletoOpen)
        Set SelectedBook = Workbooks.Open(Filename:=FiletoOpen(FileCnt))
        ShDataN.Cells.Clear
        SelectedBook.Worksheets("Client").Cells.Copy
        ShDataN.Range("A1").PasteSpecial xlPasteValuesAndNumberFormats
        SelectedBook.Close False

        'locate last empty row in Monthly Table
        lastRow = ShMN.Cells(Rows.Count, 1).End(xlUp).Row + 1

        'locate last row in the new data
        LastTemp = ShDataN.Cells(Rows.Count, 1).End(xlUp).Row


        'do while to find matching headers before copy paste
        c = 1
        Do While ShMN.Cells(1, c) &lt;&gt; ""

        Set GetHeader = ShDataN.Rows(StartRowTemp).Find _
        (What:=ShMN.Cells(1, c).Value, LookIn:=xlValues, MatchCase:=False, lookat:=xlWhole)
        If Not GetHeader Is Nothing Then
            ShDataN.Range(ShDataN.Cells(StartRowTemp + 1, GetHeader.Column), ShDataN.Cells(LastTemp, GetHeader.Column)).Copy
            ShMN.Cells(lastRow, c).PasteSpecial               ' row 2 modified to lastRow
            ShMN.Rows("2:" &amp; ShMN.Rows.Count).ClearFormats
'            Call Range_Case
             'to change the case on column Client's name after copying


        End If 'get Header
        c = c + 1
       Loop

        Next FileCnt

Debug.Print Timer - Tm
Dim MyArr As Variant, FinalArr() As Variant, i As Long
                Set MyRange = ShMN.Range("B2:B" &amp; ShMN.Cells(Rows.Count, 2).End(xlUp).Row)

                'For Each cell In MyRange
                'cell.Value = UCase(cell)
                'Next cell

                MyArr = MyRange.Value
                ReDim FinalArr(LBound(MyArr, 1) To UBound(MyArr, 1))
                For i = LBound(MyArr, 1) To UBound(MyArr, 1)
                FinalArr(i) = UCase(MyArr(i, 1))
                Next

                MyRange.Value = FinalArr

        'MsgBox "Data imported sucessfully", vbInformation, "General Information"

    End If 'isArray
    ShDataN.Cells.Clear

    'With ShNote
    '    .Select
    '    .Range("A1").Select
    'End With

    Application.ScreenUpdating = True
    Application.EnableEvents = True
    Application.DisplayAlerts = True

Debug.Print Timer - Tm
End Sub


Finally I tried the case changing with arrays to minimize excel cell operations as my ethic. You may use your process (commented out). it hardly affect performance in this case.