Additionally, could Obama have applied for and made amendment to his vital records, to change his legal name from Barry Soetoro to Barack Hussein Obama in 1988 if his vital records are held by the family court system under seal?
Yes, because it would only be his original that was under that seal.
Same process as when I got married, really. It just changes the name on the current certificate. Now, bear this in mind though — maybe this is what you meant — a legal name change would NOT change what appears on his original BC, or in any of the other files.