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In this dialogue, John and Sofia are speaking to each other informally. Thus they use the ти form of [you] rather than the ви form.
There are two ways to ask [What's your name?]:
Як вас звати? is the formal way.
Як тебе звати? is the informal way.
To ask the [Why?] questions, you can use the Ukrainian word Чому?.
When expressing your profession, again note that the [is / am / are] verb is omitted. Thus to say, [I am a programmer], you say simply:
Я програміст, which means literally [I programmer].
To ask someone's profession, Ukrainians use the word [how]. Note that the word [how] has a version for masculine nouns Як, and a version for feminine nouns Яка. Since професія is a feminine noun, we use the Яка form and say:
Яка твоя професія?. Note that in this question, the [is] verb is omitted.