Non-exact Vlookup with multiple search criteria - Microsoft Excel

Non-exact Vlookup with multiple search criteria - Microsoft Excel

I'm having a problem extracting some date from a table in Excel. The data
is in the format shown in the diagram below:
Name---------------------------First Name------------------- Surname
Billy Peter Hunt---------------Tim---------------------------Smith
Chris Paul Smith---------------Brad--------------------------Johnson
Dave Colin Jones---------------Karen-------------------------Perry
Dr James Clyde Watt------------Dave--------------------------Jones
John Phil Cross----------------Chris-------------------------Smith
Kelly Holmes-------------------Hector------------------------Baxter
Norman Bryce-West--------------Billy-------------------------Hunt
For each person listed in the First Name and Surname columns (e.g. "Tim
Smith", "Brad Johnson" etc) I want to be able to search through the Name
column, for the first cell that contains both the First Name AND Surname
of the person being searched for, and output the results into a new
column.
As there are lots of middle names, titles and double-barreled surnames in
the Name column, I can't use an exact match search. I need to search the
contents of each cell to see if they have any matching sub-strings.
I've found that I can use Vlookup with wildcards to search based on either
the First Name OR Surname columns, but I can't figure out how to use both
columns simultaneously as search criteria.
Any help with this would be much appreciated. I've been typing all sorts
into Google and making lots of frustrated grunts to no avail.