Currently, I live in Indonesia, I bought a house and registered it under my son's name since he has an Indonesian passport while I don't. Is there a way to register a house under my name if I live there and married from there?
According to http://www.globalpropertyguide.com/Asia/indonesia/Buying-Guide, the general answer is that you can't really, and that your current arrangement is probably the best you can do. Apparently what foreigners do is either buy a right to use property or buy a convertible lease to a condominium (the lease basically is a contract which gives you the condo at such a time as it becomes legally possible to do so).
What you have to understand is that Indonesia is outright hostile to major assets of the country being held by foreigners and this is even more true of real estate than it is in business. Real estate, unlike business, is a permanent and limited asset, and so this hostility enters with special force there. As Sukarno pointed out, Indonesia in the 1920's was poor not because the land was poor, but because the assets were all owned by the Dutch. This insight is the driving force of Indonesian economic policy today and it is extremely important to understand to navigate these.
In general I would add that there are a couple of other ways to do things:
Purchase and assignment with a contract which provides you your interest. This is typically the way foreigner-operated small businesses are operated also in Indonesia.
Lease with some sort of value rights.
In general the case here is that while you may not hold title, you can effectively secure the rights from title that you want through contract, and legal ownership and use are thus effectively separated. As a foreigner in Indonesia you are going to have to be comfortable with that separation.