How do you do is just a set phrase for introducing yourself to someone when you meet them for the first time. You can respond with, "Pleased to meet you" then introduce yourself by name, if they don't already know who you are.

You would reply just as you would to "How are you doing".

As Hilary says, 'How do you do?' is simply a set phrase used when meeting someone for the first time. It is not a question. The correct response is to repeat 'How do you do?'