Thoughts very rarely translate into language in completely formed phrases. Sometimes it takes a stab or two to articulate what exactly it is you're trying to say.
The opposite, however, is also true: Incomplete language can and often does imply perfectly complete ideas, and sometimes an incomplete phrase is the most natural way to express something. And Japanese is a language where this seems especially true.
One of the very first phrases students of the language learn is お名前は？ (O-namae wa?, "[What's] your name?") This is not a complete sentence grammatically. You can add 何ですか？ (Nan desu ka?, What is?) and complete the sentence, but it isn't necessary; everyone in the conversation knows what's being asked, so in the interest of economy, it gets left out.