ALTER OPERATOR CLASS name USING index_method RENAME TO newname ALTER OPERATOR CLASS name USING index_method OWNER TO newowner
ALTER OPERATOR CLASS changes the definition of an operator class.
You must own the operator class to use ALTER OPERATOR CLASS. To alter the owner, you must also be a direct or indirect member of the new owning role, and that role must have CREATE privilege on the operator class's schema. (These restrictions enforce that altering the owner doesn't do anything you couldn't do by dropping and recreating the operator class. However, a superuser can alter ownership of any operator class anyway.)
There is no ALTER OPERATOR CLASS statement in the SQL standard.