LISTING FILES IN FOLDER - INCORRECT ORDER

[p45cal]

Try the following (you don't need the FileSearch Class):

Sub blah()
Set fso = CreateObject("Scripting.FileSystemObject")
myPath = ThisWorkbook.Path & Application.PathSeparator
For Each R In Range("A1", Range("A" & Rows.Count).End(xlUp))
  Z = R.Value    '"06.Elephants"
  dot = InStr(Z, ".")    '3
  q = Left(Z, dot - 1)    '"06"
  OldName = "File" & q & ".pdf"    '"File06.pdf"
  NewName = Z & ".pdf"    '"06.Elephants.pdf"
  If fso.fileexists(myPath & OldName) Then Name fso.getfile(myPath & OldName) As myPath & NewName
Next R
End Sub

This goes through the names in column A of the active sheet

• Takes everything to the left of the first dot in those names (including leading zeroes) and
• uses it to construct a filename to look for in the same folder as the workbook is in of the ilk: File06.pdf then
• if it finds one renames it to what's in the cell in column A with .pdf tacked on..

Bear in mind you said "files are just called File1.pdf, File2.pdf etc." whereas your picture suggests files are called File01.pdf, File02.pdf etc.

ps.the above can be shortened to:

Sub blah2()
Set fso = CreateObject("Scripting.FileSystemObject")
myPath = ThisWorkbook.Path & Application.PathSeparator
For Each R In Range("A1", Range("A" & Rows.Count).End(xlUp))
  OldName = myPath & "File" & Left(R.Value, InStr(R.Value, ".") - 1) & ".pdf"
  If fso.fileexists(OldName) Then Name fso.getfile(OldName) As myPath & R.Value & ".pdf"
Next R
End Sub