This is a charade - multiple parts are joined together in sequence to form the answer word.
Break this into three parts: 'Cute' gives you the first part, 'name' becomes a single letter (N), and 'that is' has a Latin abbreviation. Put them together in order.
Answer: TWEENIE | TWEE (cute) + N (name) + IE (Latin abbreviation for 'that is' - id est)