Yes, it’s clear that a baby born in Kenya with the last name “Obama” in that time frame could easily refer to another child entirely. And in fact does, since there is nothing indicating that Zero was born in Kenya, especially since his father is not the Kenyan Obama!
Odera, the friend of the Kenyan, told the author Peter Firstbrook that Kezia had a child in her husband’s absence. The name of that child would have been registerd as Obama, and legally, even though he was in Hawaii, that child would have been his.
The name of that child would be what is recorded in the UK archives. There was an investigation conducted by the Kenyans themselves, and they wrote they couldn’t understand why there appeared to be a birth record for October, 1961 for an Obama.
They apparently felt that the family was hiding something.
They were probably trying to hide the identity of the father. There were actually several children of doubtful paternity born after the kenyan left Nairobi and after he returned to Kenya - they sort of hoovered them up - by telling us that Kezia and the old man continued to ‘have relations’
When in fact, Ruth tells Sally Jacobs that Kezia’s first two, Malik and Auma, lived in Nairobi with them and went to a private school there, and Kezia wasn’t allowed to visit them. The kenyan kept her away from his son and daughter.
Trying to create a ‘he was born in Kenya’ story out of that mess would appear to be a total waste of time.