That's a great question. I guess it depends on the context, but I usually try to throw a fun fact in there as well ("My name is Lior and I'm a dog person", or "My name is Lior and I really like cooking and baking").
Definitely depends on the setting and what the actual goal is when answering. For example, if this question were proposed to you in an interview type setting, I like to stick with something basic like your name. I know this may seem like an awkward approach but it has helped me in a jam in a number of ways.
Furthermore, by your name, I mean using positive adjectives to describe yourself and following up with a brief description as to why. Using your name as a reference:
T - Trustworthy (At my last job, my supervisor was very trusting of me to deliver products and projects in a timely manner to meet crucial deadlines)
A - Ambitious (I am definitely someone who does not wait to take action. I see a problem and I make a decision that would not only benefit me, but would be beneficial to the team as well.)
So on and so forth..hope this was able to grant you some clarity in your question. Good luck! =D