There is no name change for Obama in Hawaii at the Lt.Governor office according to public records requests. That would not include adoption records which are sealed.
http://hawaii.gov/ltgov/office/name
In the files that were made public, SAD claimed not to have gone by other names which we know is incorrect since there are places where she went by the last name Obama. It’s doubtful that her son, Soebarkahm would have felt compelled to make a legal name change.