Ncuti Gatwa demonstrates how to pronounce his name. Source video from the official Doctor Who YouTube page:
Ncuti is Rwandan and Scottish. He was born in Kigali, Rwanda. He grew up from age 2 in Edinburgh and Dunfermline, Scotland. He studied acting at the Royal Conservatoire of Scotland.
The name Ncuti appears to be of Kinyarwandan origin, but that has not been confirmed.
The origins of the Gatwa are unclear, but it appears to be Kiswahili.