Sql Substring and Search String
How about something like this..

DECLARE @Contact   VARCHAR(150) --Value for the full contact name
DECLARE @ContactID INT

SELECT @ContactID = contact_id
  FROM supplier_contacts
 WHERE (first_name = SUBSTRING(@Contact, 1, CHARINDEX(' ', @Contact) - 1) AND
       last_name = SUBSTRING(@Contact, CHARINDEX(' ', @Contact) + 1, LEN(@Contact)))
or
first_name = SUBSTRING(@Contact, 1, CHARINDEX(' ', @Contact) - 1)