I don't know about the name of the document , but see below what you need to do (register the marriage certificate at the Indonesian Embassy , then in Indonesia) . Better check , at the Indonesian Embassy , to know the details .
(partial copy of the info at http://www.expat.or.id/info/gettingm...indonesia.html)
[..Indonesian citizens who have married abroad (outside Indonesia) are obligated to register with an appropriate Indonesian government consular office (consulate or embassy) in the country where the marriage took place, in order to report this marriage officially to the Indonesian government.
A report must also be made to the appropriate government authority in your hometown in Indonesia in order to assure that your marriage is legal under Indonesian law. If you are Muslim, you report your overseas marriage to the Kantor Urusan Agama (KUA) in Indonesia, if you are from another religion, you report to the Catatan Sipil in the hometown of the Indonesian spouse. Without reporting in this way, you are not considered married by the Indonesian government! This should be done, at the latest, 30 days after the Indonesian citizen returns to Indonesia. The fine for a late registration is of a maximum of IDR 1.000.000 and is further regulated by regional regulations...]