PostgreSQL:

ALTER INDEX

ALTER INDEX [ IF EXISTS ] name RENAME TO new_name
ALTER INDEX [ IF EXISTS ] name SET TABLESPACE tablespace_name
ALTER INDEX [ IF EXISTS ] name SET ( storage_parameter = value [, ... ] )
ALTER INDEX [ IF EXISTS ] name RESET ( storage_parameter [, ... ] )
ALTER INDEX ALL IN TABLESPACE name [ OWNED BY role_name [, ... ] ]
SET TABLESPACE new_tablespace [ NOWAIT ]

Example

ALTER INDEX distributors RENAME TO suppliers;
ALTER INDEX distributors SET TABLESPACE fasttablespace;

ALTER INDEX distributors SET (fillfactor = 75);
REINDEX INDEX distributors;