Its a case of when you go to Rome, do as the Romans do.
In most Kenyan communities, people have 3 names:
1. The first name is usually a Christian name, like John or Joseph. Nowadays people are shunning this 'western-sounding' for indigenous African names.
2. The second name is usually the given name. This will vary from community to community. For example, some communities may name you after a goat, or thunder, or an act. Kikuyus name their children after relatives, whether dead or alive. Its the very rare case where you dont name your child after a relative, for example in mixed marriages.
3. The third name is the 'family name' otherwise referred to as surname in Western culture. The family name refers to the nuclear family as constituted by a father, one or more wives, and their children. The 'owner' of the family is the husband, thus every member is named after his given name, that is the middle name.
The concept of surname as exemplified in Western cultures can best be compared to a cla name (or a subclan). For example, you may say you are John Njoroge Kamau of Mbari ya Kangethe. The Kangethe part is what Westerners refer to as Surname. The concept does not, however, exist in Kikuyu (and most Kenyan) tribes and we have opted to make the family name the Surname.
In These Western cultures, the surname is inherited by all descendants of the particular Originator of the surname. Thats why they are able to trace their lineages so easily. You can however change your surname and that of your child but you will require a legal process for it.
Gũtirĩ wairegi ũtũire.