I don’t believe there was a “Republic of Kenya” which could appoint Principal Registrars in 1961.
Sorry for my mistake - no coffee yet. The document was issued BY the Republic of Kenya after its establishment in 1963, so that's not a problem, per se. This document is quite interesting, but given its importance, I would imagine that its provenance would have to be established by the Commonwealth Office in London and/or the Government of Kenya.
The names are hardly what one would call ‘Kenyan’ - Miller and Lavender.
No problem. These would have been “principal registrar” etc. under the British Colonial government. That would readily explain why they have English names.
The 1964 document is describing the process that took place in 1961 at the hospital and in colonial government offices. If indeed BO was born in Mombansa, Aug. 4, 1961, then the official recording of would have been done under the British colonial government.