Rename Cell to Various Different Sheet Titles

If you are on M365, you can use this lambda formula, which does not require saving the file as macro-enabled file: https://jkp-ads.com/articles/excel-lambda-function-examples.aspx#name_of_worksheet_in_cell 

You've gotten a number of proposals for how to achieve what you asked, and if one (or more) of those satisfy you fully, fine.

When I read requests like this--where it's obvious (or seems to be so; forgive me if I'm wrong) that you are creating a sheet for each month of the year--I will often first turn the question back and ask "Why?" Why, specifically, are you designing this workbook with a separate sheet for each month? 

I've seen many a time when that approach is undertaken because that's how we did it on paper ledger sheets, so it just makes sense to automate it with the same structure, assuming Excel can make (as it can) the links to summarize from monthly into quarterly or annual reports. HOWEVER, Excel has marvelous capabilities to summarize data on a monthly, quarterly, or annual basis, working from a single database of transactions or activities. And it's generally more straightforward if you do things that way.

Think of it as letting Excel do the heavy lifting. If you've continued the task of "manually" storing data on a month-by-month basis, you're doing a fair amount of work unnecessarily.

So my next question: is it possible that you could benefit from re-thinking the basic design of your workbook. (Just a suggestion. Feel free to totally ignore.)

"Having to do it manually at the scale required would be quite difficult."
That seems unlikely.  The "scale" is one new worksheet at a time.

But perhaps you meant that manually creating the initial list of existing worksheets would be tedious.  Yes, it could be (for example, if you inherited a workbook with hundreds of worksheets).  This post suggests how that could be done readily.

A better-behaved macro would not modify an entire column on the active worksheet (however important that may be!) without user confirmation, leaving no way to undo the data change.  So consider this code instead:

Sub LoadListOfWorksheets()
'   This macro creates a list of the worksheets in the active workbook
'       into column A (see the constant below) of the active worksheet,
'       subject to confirmation by the user.

    Const strCOLUMN_ID = "A"    'for output
    Const in4FIRST_ROW_TO_USE As Long = 2   'for output
    
    Dim objWkbook       As Workbook
    Dim objListWksht    As Worksheet
    Dim strFullColumn   As String   'identifies the range
    Dim in4CellsWithContent As Long '…within the range
    '  --   Related to the user confirmation:
    Dim dstrMessage     As String
    Dim in4Icon         As Long
    Dim in4UserResponse As VbMsgBoxResult
    '  --   Indexes, etc.:
    Dim in4Wksht        As Long '…within the Sheets collection
    Dim in4OutputRow    As Long
    
    '----   Capture information and do preparations.
    Set objWkbook = ActiveWorkbook
    Set objListWksht = ActiveSheet
    '
    strFullColumn = strCOLUMN_ID & ":" & strCOLUMN_ID
    
    '----   Get user confirmation.
    in4CellsWithContent = WorksheetFunction.CountA( _
            objListWksht.Range(strFullColumn))
    dstrMessage = "Is it OK to put the worksheet names into column " _
            & strCOLUMN_ID _
            & vbCrLf & " of worksheet " & objListWksht.Name _
            & vbCrLf & " in workbook " & objWkbook.Name & "?"
    If in4CellsWithContent > 0 Then
        dstrMessage = dstrMessage & vbCrLf & vbCrLf _
                & "WARNING: Column " & strCOLUMN_ID & " has " _
                & Format$(in4CellsWithContent, "#,###,###,##0") _
                & " cell" & IIf(in4CellsWithContent = 1, "", "s") _
                & " that contain" & IIf(in4CellsWithContent = 1, "s", "") _
                & " some content.  That content will be erased !!"
        in4Icon = vbExclamation
    Else
        in4Icon = vbQuestion
    End If
    in4UserResponse = MsgBox(dstrMessage, in4Icon Or vbYesNo _
            Or vbDefaultButton2, "Load List of Worksheets")
    If in4UserResponse = vbNo Then Exit Sub
    
    '----   To improve performance of the remaining code, turn off
    '       screen updating.
    Application.ScreenUpdating = False
    
    '----   Clear any existing content.
    With objListWksht.Range(strFullColumn)
        .ClearContents
        .NumberFormat = "@" 'to prevent Excel from converting certain _
                worksheet names to a date or number or Boolean
    End With
    
    '----   Create an unsorted list of all worksheet names.
    in4OutputRow = in4FIRST_ROW_TO_USE
    For in4Wksht = 1 To objWkbook.Sheets.Count
        objListWksht.Range(strCOLUMN_ID & in4OutputRow).Value = _
                objWkbook.Sheets(in4Wksht).Name
        '
        in4OutputRow = in4OutputRow + 1
    Next in4Wksht
    
    '----   Restore setting(s).
    Application.ScreenUpdating = True
End Sub

I will leave it as an exercise for you to write worksheet names into one row, rather than into one column.

Note that this macro would not even have to be stored in the relevant workbook.  You could place it into your Personal.xlsb workbook.

As for automatically updating a list of workbooks (whether in a range of cells or an Excel table), that's complicated.  See the attached workbook for more information and example VBA code.

Edit: fixing another example of the forum dropping the file that I attached

Edit: trying a third time

Edit: and a fourth time

So my approach would be to reserve a cell on each sheet for the sheet name.  For example cell A1 could be:

=LET(path,CELL("filename",A1),RIGHT(path,LEN(path)-SEARCH("]",path)))

Then make sure you have all the sheets 'bound' by a known sheet name.  For example lets say you always have JAN first and the last sheet is SUMMARY and you insert months inbetween as the year goes by then:

=DROP(HSTACK('JAN:SUMMARY'$A$1),,-1)

where that will 'stack' all the sheet names (each found in cell A1 of each sheet) and then drop that last one from this SUMMARY sheet.