The correct answer is Option D.
IS is used when we refer to a single person or thing. NAME is singular, hence IS is the correct answer.
From NO in the second part of the given question, we know that the name is not Eliza. This is why ISN'T is the answer. It is a contraction of 'is not.'
The remaining options are incorrect because:
Option A: This is grammatically incorrect.
Option B: The reference is to the name so the pronoun will be a neuter gender pronoun i.e. IT. SHE is a feminine pronoun.
Option C: IT IS NOT is the extension of ISN'T but in conversation, ISN'T is more appropriate to use.
Hence Option D is the correct answer.