Hi Tia,
 I don't know about  formula, but here a macro that solve your problem.
enjoy...
  Rick

Option Explicit

Public Sub Contacts()
Dim ws1 As Worksheet, ws2 As Worksheet
Dim s1Rc As Integer, s2Rc As Integer

Set ws1 = Worksheets("Sheet1")
Set ws2 = Worksheets("Sheet2")
Application.ScreenUpdating = False  '' stop screen update

s2Rc = 3        '' start row sheet 2
Do Until IsEmpty(ws2.Cells(s2Rc, "A"))
 s1Rc = 3      '' start row sheet 1
   Do Until IsEmpty(ws1.Cells(s1Rc, "A"))
      '' compare names (First + Surnmame)
       If (ws2.Cells(s2Rc, "A") & ws2.Cells(s2Rc, "B") = _
         ws1.Cells(s1Rc, "B") & ws1.Cells(s1Rc, "A")) Then
          '' copy contact from sheet1 to sheet2
           ws1.Cells(s1Rc, "C").Copy ws2.Cells(s2Rc, "G")
         Exit Do
       End If
     s1Rc = s1Rc + 1   '' next row sheet1
   Loop
 s2Rc = s2Rc + 1       '' next row sheet2
Loop

End Sub

Andy Wrote:

If you can make do by checking only first name or only surname ( you
cannot match both name and surname ) and then want to fill up the
contact number in Col G then you could try Vlookup. Suppose you want to
match surname. Let us assume that your table on sheet 1 has 20 rows of
data ( 1 to 20 ) then your lookup range is A1:C20. Also assume that
your table on sheet 2 starts from row 1 then formula for G1 would be
VLOOKUP(A1,sheet1!A1:C20,3). You can autofill this formula to all the
cells in G down below.

And yes one more pointer. Data in sheet 1 (A1:C20) should be sorted on
A1( Surname) in ascending order.

A V Veerkar