Your link is the Constitution with consolidated amendments to 1999. The dates and content of prior amendments is not indicated. We will need to review the 1963 enactment, if it is online. One hint, however, is that several provisions in the 1999 consolidation indicated that certain changes were to become effective December 12, 1964. The country's name was likely another one of those December 12, 1964 changes. I will keep searching.
I’ll concede the point for now, but that’s not enough determine that this document is fraudulent. It may very well have been common practice for the Kenyan government in 1964 in anticipation by placing the ‘Republic of Kenya’ on their letterhead.