If FName and LName contain NULL values, then you will need special handling to avoid unnecessary extra preceeding, trailing, and middle spaces. Also, if Address1 contains NULL values, then you need to have special handling to prevent adding unnecessary ', ' at the beginning of your address string.
If you are using SQL Server 2012, then you can use CONCAT (NULLs are automatically treated as empty strings) and IIF:
INSERT INTO TblStuff (FullName, Address, City, Zip)
SELECT FullName = REPLACE(RTRIM(LTRIM(CONCAT(FName, ' ', Middle, ' ', LName))), ' ', ' ')
, Address = CONCAT(Address1, IIF(Address2 IS NOT NULL, CONCAT(', ', Address2), ''))
, City
, Zip
FROM tblImport (NOLOCK);
Otherwise, this will work:
INSERT INTO TblStuff (FullName, Address, City, Zip)
SELECT FullName = REPLACE(RTRIM(LTRIM(ISNULL(FName, '') + ' ' + ISNULL(Middle, '') + ' ' + ISNULL(LName, ''))), ' ', ' ')
, Address = ISNULL(Address1, '') + CASE
WHEN Address2 IS NOT NULL THEN ', ' + Address2
ELSE '' END
, City
, Zip
FROM tblImport (NOLOCK);