The two ways of relating what a person has said are 1)direct and 2)indirect (reported speech).In direct speech, the original speaker's exact words are repeated. In indirect/reported speech, the exact meaning is expressed but not necessarily using the original speaker's exact words. Pronouns and possessive adjectives usually change from first or second person to the third person except when the speaker is reporting his own words. Sometimes a noun can be inserted to avoid doubt.
When we turn direct questions and exclamations into indirect speech, they are converted to affirmative statement .( ? and ! is not used).
Option D is correct as when we convert the given direct question to indirect speech which starts with the question word what, what is used in the reported speech, simple present is changed to simple past, present continuous to past continuous, your to her, I to she, and you to him.
The other options are wrong as your is not changed to her,simple present can't be used, simple present continuous tense can't be used.
The correct answer is D)Sam asked what her name was to which Sue replied that she was not going to tell him