PostgreSQL:

ALTER FUNCTION

Topic

ALTER FUNCTION name ( [ [ argmode ] [ argname ] argtype [, ...] ] )
action [ ... ] [ RESTRICT ]
ALTER FUNCTION name ( [ [ argmode ] [ argname ] argtype [, ...] ] )
RENAME TO new_name
ALTER FUNCTION name ( [ [ argmode ] [ argname ] argtype [, ...] ] )
OWNER TO new_owner
ALTER FUNCTION name ( [ [ argmode ] [ argname ] argtype [, ...] ] )
SET SCHEMA new_schema

where action is one of:

CALLED ON NULL INPUT | RETURNS NULL ON NULL INPUT | STRICT
IMMUTABLE | STABLE | VOLATILE
[ EXTERNAL ] SECURITY INVOKER | [ EXTERNAL ] SECURITY DEFINER
COST execution_cost
ROWS result_rows
SET configuration_parameter { TO | = } { value | DEFAULT }
SET configuration_parameter FROM CURRENT
RESET configuration_parameter
RESET ALL

Example

ALTER FUNCTION sqrt(integer) RENAME TO square_root;
ALTER FUNCTION sqrt(integer) OWNER TO joe;
ALTER FUNCTION sqrt(integer) SET SCHEMA maths;
ALTER FUNCTION check_password(text) SET search_path = admin,
pg_temp;