“Ko wai tō ingoa?” is used to ask someone what their name is.
If a person asks you, “Ko wai tō ingoa” then you would reply “Ko ... taku ingoa.” It is impolite in Māori to ask "Ko wai koe?", or "Who are you?"
For example, let’s pretend your name is Mere Wehipeihana.
Ko wai tō ingoa?
What is your name?
You could reply: Ko Mere taku ingoa.
My name is Mere.
Ko Mere Wehipeihana taku ingoa.
My name is Mere Wehipeihana.
Ko wai tō ingoa whānau?
What is your family name?
Ko Wehipeihana taku ingoa whānau.
Wehipeihana is my family name.
Pātai atu ki ia tangata o Te Whanake, “Ko wai tō ingoa?”
Ask each character of Te Whanake – “What is your name?”