Modifying the records to contain quotes would be a disaster; you don't use the data only for export. Further, in theory you'd have to deal with names like:
Thomas "The Alley Cat" O'Malley
which presents some problems.
In Standard SQL, you'd use doubled-up single quotes to enclose single quotes (with no special treatment for double quotes):
'"Thomas "The Alley Cat" O''Malley"'
Some DBMS allow you to use double quotes around strings (in Standard SQL, the double quotes indicate a 'delimited identifier'; SQL Server uses square brackets for that), in which case you might write the string as:
"""Thomas ""The Alley Cat"" O'Malley"""
Normally, though, your exporter tools provide CSV output formatting and your SQL statement does not need to worry about it. Embedded quotes make anything else problematic. Indeed, you should usually not make the DBMS deal with the formatting of the data.