Reversing Names In Place

Sorry. If you copy/paste the first formula in my comment below that begins with =MID(A1,... you must replace the 3 non-breaking space characters with regular space characters.

My Excel Toolbox includes the following functions (derived from VBA) that might be useful for manipulating text as described in the Tip:
=FindRev(FindText,WithinText,[StartNum],[CaseSensitive])
=IsLike(Text,Pattern)
=Between(Text,BeginAfter,EndBefore,[CaseSensitive], [Direction])
Assuming a name like "John J. D. Smith" is in cell A1, here is a cell formula that performs like Willy's Reverse() macro:
=MID(A1,FindRev(" ",A1)+1,999)&", "&LEFT(A1,FindRev(" ",A1)-1)

My Excel Toolbox also includes these dynamic array functions:
=SplitText(Text,[Delimiter],[CaseSensitive],[Limit],[Remainder])
=ArraySize(Var)
=GetCols(RangeArray, ParamArray Cols())
Assuming a name like "John J. D. Smith" is in cell A1, here are cell formulas that perform tasks like Peter's SplitRev() macro:
Cell A2 (first name):
=GetCols(SplitText(A1),1)
Cell A3 (last name):
=GetCols(SplitText(A1),ArraySize(SplitText(A1)))
Cell A4 (middle names, if any):
=TRIM(Between(A1,A2,A3))

See https://sites.google.com/view/MyExcelToolbox/

One small drawback with InstrRev is that it only works for two word names. William S. Morris is returned as Morris, William S. The Split method offers a bit more control returning Morris S,, William

Sub SplitRev()
Dim c As Range, x As Variant
For Each c In Selection
x = Split(c, " ")
If UBound(x) = 2 Then
c = x(2) & " " & x(1) & ", " & x(0)
Else
c = x(1) & ", " & x(0)
End If
Next c
End Sub

Mind you it will be slower than Willy's code.

@Jeff
X = InStrRev(Cell, " ") -> X will contain the position of the last space in the string. If X contains 0, meaning there is no space in the string or de cell is blank or contains a number, the following line will be skipped avoiding an error.

Hey Willy, in your code you have 'If X Then Cell'. I don't get it: If X ... what?

This macro, half the size, does the same job:

Sub Reverse()
Dim Cell As Range, X As Integer
For Each Cell In Selection()
    X = InStrRev(Cell, " ")
    If X Then Cell = Mid(Cell, X + 1) & ", " & Left(Cell, X - 1)
Next Cell
End Sub

Flash fill is an overlooked feature that will do the name reversal really easily.
Just type what you want the result to be in the cell next to the names.
As you start to type the second name Excel should recognise the pattern and offer to complete the column for you.

This won't do it in the same column as the original data, but a quick cut then paste special values over the original data will accomplish this.