I finally figure out to accomplish what I needed. Here is how the final code looks like in case someone needs it.
Code:
Private Sub Command0_Click()
Dim rsFolders As DAO.Recordset
Set rsFolders = CurrentDb.OpenRecordset("SELECT DISTINCT [OldPath], [NewPath] FROM RenPaths")
Do While Not rsFolders.EOF
' Check that Old Path exists.
If Len(Dir(rsFolders![OldPath], vbDirectory)) > 0 Then
' Check that New Path doesn't exist.
If Len(Dir(rsFolders![NewPath], vbDirectory)) = 0 Then
Name rsFolders![OldPath] As rsFolders![NewPath]
End If
End If
rsFolders.MoveNext
Loop
rsFolders.Close
Set rsFolders = Nothing
End Sub