Closely tied into the Indonesian Citizenship Myth is the story that Lolo Soetoro formally adopted Barack Obama, changing his name to "Barry Soetoro" or “Soebarkah".
The problem with this is that the people promoting also tend to empathize Lolo Soetoro being Muslim (Indonesia is 86.1% Muslim) - and THAT touches off a problem, as the people promoting this don't know or understand how Islam deals with adoption. (islam.about.com)
(Bold face mine)
"...Nor has He made your adopted sons your (biological) sons. Such is (only) your (manner of) speech by your mouths. But Allah tells (you) the Truth, and He shows the (right) Way. Call them by (the names of) their fathers; that is juster in the sight of Allah. But if you know not their father's (names, call them) your brothers in faith, or your trustees. But there is no blame on you if you make a mistake therein. (What counts is) the intention of your hearts. And Allah is Oft-Returning, Most Merciful." (Qur'an 33:4-5)"
Notice that line - "Call them by (the names of) their father, that is juster in the sight of Allah"
Family is important within Islam. And one's family ties are considered to be sacrosanct. Even if an adoption took place, Obama's name would not have been changed because it would have been seen as an affront to both Obama's father's family AND to Allah.
That's simply not done.
The Islamic laws on adoption are called "Kafala". (wikipedia)
"While raising someone's else child is allowed and, in the case of an orphan, even encouraged, the child does not become a child of the new parents. This form of adoption where children retain membership to their original family is called, in Arabic: kafala. This implies for example that the new father cannot name the son after him"
Again, we come into the problem that naming Obama "Soetoro" would have been a violation of Islamic law. An adoptive child is not considered maharim, or a member of the adoptive family. While the role of an adoptive parent is honored, (Muhammad himself adopted a child, Zayd ibn Harithah) (wikipedia), the child is always seen as a member of the biological father's family, should that family be known. Which is the case with Barack Obama, Sr. and his family.
It's more of a foster-child situation than an adoptive child as per Western definitions of such. The adopted child maintains their ties to their fathers family. Again, Islamic laws on such are quite clear. (islam.about.com)
"The guardian/child relationship has specific rules under Islamic law, which render the relationship a bit different than what is common adoption practice today. The Islamic term for what is commonly called adoption is kafala, which comes from a word that means "to feed." In essence, it describes more of a foster-parent relationship. Some of the rules in Islam surrounding this relationship:
*An adopted child retains his or her own biological family name (surname) and does not change his or her name to match that of the adoptive family.
*An adopted child inherits from his or her biological parents, not automatically from the adoptive parents.
*When the child is grown, members of the adoptive family are not considered blood relatives, and are therefore not muhrim to him or her. "Muhrim" refers to a specific legal relationship that regulates marriage and other aspects of life. Essentially, members of the adoptive family would be permissible as possible marriage partners, and rules of modesty exist between the grown child and adoptive family members of the opposite sex.
*If the child is provided with property/wealth from the biological family, adoptive parents are commanded to take care and not intermingle that property/wealth with their own. They serve merely as trustees."
Simply put, under Islamic law and practices, even if an adoption took place, (and remember, there's never been any evidence of such), Obama would have never took on the last name of Soetoro. Such a think would have been unthinkable to the majority of Muslims, and frowned upon at best in an Islamic-majority country. Lolo Soetoro AND Barack Obama, Sr. would have had both been willing to openly and publically break with Islamic law and custom in their own countries and cultures to do so - and that's just not likely.
As such, I have to count this myth as busted.