Kenya became a republic two years after Obama was born, yes, and Obama’s original Kenyan birth certificate would not have “Republic of Kenya” on it, but remember that the document is a “certified copy” - not the original.
This certified copy was prepared on February 17, 1964, as indicated on the bottom of the page, and this explains the term “Republic of Kenya” on the form.
So anyone claiming this is a fake because of the date Kenya became a republic simply isn’t thinking things through.
It became independent on Oct. 17, 1963 nearly TWO months earlier than the rest of Kenya. They called themselves the "Republic of Kenya" in 1963, before the rest of the country was known by the same name: