British East Africa Protectorate, or something like that.
The Kenya Colony.
European and Arab presence in Mombasa dates to the Early Modern period, but European exploration of the interior began only in the 19th century. The British Empire established the East Africa Protectorate in 1895, from 1920 known as the Kenya Colony.
http://www.chacha.com/question/what-was-kenya-called-before-1964
They could have just called it Kenya I suppose.