How do you introduce yourself as a Scrum Master?

By being myself, and radiating a welcoming atmosphere

"Hi, I'm a Scrum Master and my name is Daniel."  Yeah is sounds like a flippant answer but it really is how I introduce myself.  I then start discussing Scrum with them in order to see how much they know. I ask them if I can fill in a few gaps of their knowledge. That way as I start work with them and continue to interact with the team, they start to see what a Scrum Master really is. 

As @Xander said, don't try to be anyone you aren't.  Be yourself, be welcoming, be an example of Scrum Values. If you want people to know you and what your job is about, let them see it instead of trying to tell them. 

Welcoming new team members is actually a very interesting topic.

For me, new team members typically start by attending a retrospective, which we then use to get to know each other and discuss how the team works and how it has been doing recently. As Scrum is about people, about welcoming changes and about openness, and the Retro has the entire team present, I consider the retro a great ceremony to get to know each other and discuss the roles and workflow of the team, its great powers, its hurdles, etc., with the new team member, so you immediately start building trust, respect and openness.

It typically breaks the ice if the "newbie" is immediately warmly welcomed, fully included in the discussion and immediately inspired and appreciated to speak his/her mind. After all, (s)he can do nothing really wrong yet in his/her first few hours, and there's no better time to encourage courage than immediately at the beginning.

Come to think of it, maybe it could be a stimulating idea to ask the joiner to come up with the first "high priority process improvement" (as discussed in the Sprint Backlog chapter of the Scrum Guide) by the end of that first retro. You know, before (s)he is trudging the same blinkered paths that the rest of the team has been wearing out ;)

As for introductions... Yeah, I'm with Daniel and Xander :)

I want to know from the community about how do they introduce themselves as a scrum master...

Try to do it with quiet efficiency. The challenge lies in introducing Scrum, rather than yourself. This can be especially true in places where familiarity with agile practice is assumed.

I usually get introduced ;-). I don't like to be that formal and I think introductions to the team and way of working are far more important. Those are the people with whom you should be working together.

Thanks All for your inputs. I really liked the idea of having the newbie start by attending the retrospective. :)