I've often heard it in business meetings, practically never in daily life situation. Even though, I think it's just stereotype, because in spoken English there're no restrictions :) When you first meet person in formal situation, you'd better stick with the rules. It's kinda part of tradition/protocol of meeting, so if you say something different in reply, it won't be expected.

You can say, "Hello my name is Irina, nice to meet you. ' The other person may reply, ' Hi my name is Ivan. Good to meet you too Irina. How are things going in your company?'

Although you can use How Do You Do each time when you greet people, you'd better use it in a first meeting with someone since it is frequently used under this circumstance. And that can meet English language using custom.During my school year, my teacher told me that this phrase is one of the formal expression in greeting somebody. In our daily life, we get to use How Are You instead. That's why you could seldom hear how do you do in daily greetings.

yes! same like how are you? or wass up?

You can greet people by asking "how do you do? " at any time during the day or night. The possible answers to how do you do? How do you do? Fine! how about yourself?