PostgreSQL

ALTER ROUTINE name [ ( [ [ argmode ] [ argname ] argtype [, ...] ] ) ]
    action [ ... ] [ RESTRICT ]
ALTER ROUTINE name [ ( [ [ argmode ] [ argname ] argtype [, ...] ] ) ]
    RENAME TO new_name
ALTER ROUTINE name [ ( [ [ argmode ] [ argname ] argtype [, ...] ] ) ]
    OWNER TO { new_owner | CURRENT_USER | SESSION_USER }
ALTER ROUTINE name [ ( [ [ argmode ] [ argname ] argtype [, ...] ] ) ]
    SET SCHEMA new_schema
ALTER ROUTINE name [ ( [ [ argmode ] [ argname ] argtype [, ...] ] ) ]
    DEPENDS ON EXTENSION extension_name

where action is one of:

    IMMUTABLE | STABLE | VOLATILE
    [ NOT ] LEAKPROOF
    [ EXTERNAL ] SECURITY INVOKER | [ EXTERNAL ] SECURITY DEFINER
    PARALLEL { UNSAFE | RESTRICTED | SAFE }
    COST execution_cost
    ROWS result_rows
    SET configuration_parameter { TO | = } { value | DEFAULT }
    SET configuration_parameter FROM CURRENT
    RESET configuration_parameter
    RESET ALL

ALTER ROUTINE foo(integer) RENAME TO foobar;