Birth Certificate Anomaly - How could have Obama's father have been born in a country that did not yet exist?

http://www.whitehouse.gov/sites/default/files/rss_viewer/birth-certificate-long-form.pdf

The birth certificate that the White House released lists Obama's birth as August 4, 1961. It also lists Barack Hussein Obama as his father. No big deal, right? At the time of Obama's birth, it also shows that his father is aged 25 years old, and that Obama's father was born in "Kenya, East Africa". This wouldn't seem like anything of concern, except the fact that the country "Kenya" did not even exist until 1963, two whole years after Obama's birth, and 27 years after his father's birth. How could have Obama's father have been born in a country that did not yet exist? Up and until Kenya was formed in 1963, it was known as the "British East Africa Protectorate".
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December 12, 1963: : Kenyan independence day.
1964: The Republic of Kenya (Jamhuri ya Kenya) is formed with Kenyatta as president and Oginga Odinga as vice president. The party KADU dissolves and integrates with KANU. The government is without opposition. Source
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UPDATE
Folks have pointed out to me that indigenous peoples, and others,  called the territory  "Kenya" before it became the nation of Kenya.  Yes, that is true.  However, is it likley  that the State of Hawaii would recognise the existence of a county before it was founded or before it was recognized by the federal government?  The other option is to accept that Hawaii accepted what was reported to them without verification.  Which do you think is most likely?  In either case Hawaiian birth certificates are no a trustworthy source of documentation.