With the arrival of the Pakeha, they introduced surnames.
However, in the 1800's to the early 1900's, Maori developed their own system, and that was for their surname they would take the first name of their father.
This happened for a few generations, in the 1800's, so in order to find your tupuna, always look for the firstname as a surname.
The following example shows how the surnames could change over time.
NOTE: The following example is not a known whakapapa, it has been created to show how the naming conventions work. Each line represents a person, a child of the previous person on the line above.
Ariki (born in 1700's - only one name)
Maunga Ariki (born in early 1800's takes father's name as surname)
Te Awa Waiora
Waipapa Te Awa
Hone Te Awa * (born in mid 1900's)
Changing of names also still occured because of events and circumstances.
For example, the brothers Nene and Patuone who were born in the 1700's did not have a surname. Nene was baptised after Thomas Walker a local trader, but kept his name and became known as - Tamati Waka Nene. His brother, Patuone, kept his name and was baptised as Eruera Maihi Patuone. Both born of the same parents, but with different last names.
During this time also, some Maori started having a Pakeha name, as well as the Maori version of that name and their own Maori name.
If we take Hone Te Awa * in our whakapapa example above, he could also be known as John Te Awa, Hone River, John River, Hone Waipapa Te Awa or John Waipapa Te Awa.
All of the above applies also to women. Women also kept their "surnames" and did not change them when getting married. When we are talking in our whanau about whakapapa, and talk about our grandmother (born in the 1800's) we refer to her by her "maiden name" and never with the surname of our grandfather.