You are correct. The best we can say at this point is that we are not sure what Kenya would have been calling itself throughout most of 1964. At some point following independence, new blank forms would have to have been printed. At a time of political chaos, someone may well have made a best guess as to what the eventual official name of the country would be.
And how does a country declare itself a republic? There are (and have been) plenty of “people’s republics” in the world that are something else entirely.
The answer is that a country can call itself whatever it pleases.
There were many African countries that achieved their independence in the few years before Kenya did (including Algeria, Benin, Burundi, Central Africa, Chad, Congo, Madagascar, Mali, Niger, Nigeria, Sierra Leone, Tanzania, and Togo). They all called themselves “republics”. Kenya followed the trend, apparently with some confusion along the way.
I don’t see how it is possible to declare this document real or fake on the basis of the country name that appears on it.
It’s only a matter of time until a Kenyan FReeper posts his own BC from that time period. That, or any 1961 document saying Republic of Kenya will do.