Introduce yourself?In this question what should I answer

Tell the person your name.

I would tell a short clever story about myself in the third person.

A nice question. From my personal experience, I could not answer this question in a good way at the nick of the moment the question was asked. Practice was needed, of what I was going to answer. Though this is a simple question, it gives the first impression.
This is what I will do, I start with my name. Then
1. About my educational history. In 3 simple lines, no unnecessary stories
2. About my previous experience. This needs to be powerful enough and should be related to the job for which you are going to be hired.
3. (This might vary from country to country) HR's here, will want to know if you need the job and stick with the job for at least a few years. So, I give a gist about my family and people dependent on me.