PostgreSQL:

ALTER TYPE

Topic

ALTER TYPE name action [, ... ]
ALTER TYPE name OWNER TO new_owner
ALTER TYPE name RENAME ATTRIBUTE attribute_name TO new_attribute_name [ CASCADE | RESTRICT ]
ALTER TYPE name RENAME TO new_name
ALTER TYPE name SET SCHEMA new_schema
ALTER TYPE name ADD VALUE [ IF NOT EXISTS ] new_enum_value [ { BEFORE | AFTER } existing_enum_value ]

where action is one of:

ADD ATTRIBUTE attribute_name data_type [ COLLATE collation ] [ CASCADE | RESTRICT ]
DROP ATTRIBUTE [ IF EXISTS ] attribute_name [ CASCADE | RESTRICT ]
ALTER ATTRIBUTE attribute_name [ SET DATA ] TYPE data_type [ COLLATE collation ] [ CASCADE | RESTRICT ]

Example

ALTER TYPE electronic_mail RENAME TO email;
ALTER TYPE email OWNER TO joe;
ALTER TYPE email SET SCHEMA customers;
ALTER TYPE compfoo ADD ATTRIBUTE f3 int;
ALTER TYPE colors ADD VALUE 'orange' AFTER 'red';