As I wrote, a comment number is shown (following your initials) for comment balloons when you look at the Print Preview (found at File | Print) and also in an actual printout:

If you want comment numbers in Print Layout view, you will have to make use of a macro. The following one by MVP Doug Robbins can be run multiple times after you have added, removed or rearranged comments:
Sub NumberComments()
'Macro created by MVP Doug Robbins, April 2017
Dim i as Long
Dim rngComment as Range
With ActiveDocument
For i = 1 to .Comments.Count
Set rngComment = .Comments(i).Range
With rngComment
If Left(.Text, 7) = "Comment" Then
.Text = "Comment " & i & " " & Mid(.Text, Instr(.Text, "-"))
Else
.Text = "Comment " & i & " - " & .Text
End If
End With
Next i
End With
End Sub
For installation instructions, see http://www.gmayor.com/installing_macro.htm.