I am a South Indian. As per the passport my surname is Michael and my given name is Sukumar. How shold I write my expanded name (full name)- as Michel Sukumar or Sukumar Michael
This could cause some confusion to westerners because for us, Michael is usually a given name and we would expect Sukumar to be a surname.
Think of James Bond.
"My name is Bond, James Bond."
James Bond's girlfriends call him James.
James Bond's boss, M, calls him Bond.
His full name is James Bond. James (given name) Bond (surname).
In your case you could say,
"My name is Michael, Sukumar Michael.
Your friends would call you Sukumar and your boss, if being formal, would call you Michael.
Your full name is Sukumar Michael. Sukumar (given name) Michael (surname).
As I say, expect some confusion because people will expect your names to be the other way around.
Thoughts on introducing yourself.
If you meet some new people who may become friends, you can just say, "Hello, my name is Sukumar" then you can tell them your surname later when they have got used to calling you Sukumar.
If you go to a job interview, then I suggest you say, e.g.
"Good morning, my name Sukumar Michael."
If there is any confusion, just say "My surname is Michael."
"As per the passport" doesn't help in this instance. I have a friend whose name on official Indian documents (such as school records) is S. Aarthi. As a result, on official U.S. documents, including the U.S. passport she has as an immigrant, her "first name" is Sundararaman, which is actually her father's name; and her "last name" is Aarthi.
As far as common American usage goes, that's exactly backwards. Her own specific name--the name people use in referring to her, and not to any other member of her family--is Aarthi. So by American standards her "first name" ought to be Aarthi. Her family name, surname, or "last name"--the name she has in common with other members of her family--ought to be Sundararaman. Her name when written out in full ought to be Aarthi Sundararaman.
Similarly, if people call you Michael and your mother is Mrs Sukumar, then your first name is Michael, your last name is Sukumar, and your full name is Michael Sukumar. If people call you Sukumar and your mother is Mrs Michael, then your first name is Sukumar, your last name is Michael, and when written out in full, your name is Sukumar Michael. Your question doesn't actually give us enough information for us to be sure. But I'm guessing that your own name is Sukumar, and your family name ("surname") is Michael.
Note that if you choose to write out your full name as "Sukumar Michael" because people call you Sukumar and your family is the Michael family, but your Indian passport follows the South Indian convention of putting the family name first and has you as "Michael Sukumar", then you may have some explaining to do should you ever choose to get an American document such as a marriage certificate or that holy grail, a U.S. Passport.
Americans are often aware that the Chinese put their family names first; an actress well known as Zhang Ziyi in China is sometimes called Ziyi Zhang in the U.S., because by U.S. convention her given name, the name unique to her and not shared with the rest of her family, is Ziyi. You'll have some luck if you say "My given name is Sukumar, and Michael is my family name, but in South India, as in China, the family name is typically mentioned first, unlike in the U.S. So even though my Indian passport says Michael Sukumar, my name on official American paperwork needs to be Sukumar Michael, with my given name first and my family name last."
Hope this helps.
This is a common dilemma for the South Asians. Traditionally, they write their names starting with the initialized first name of their father, placing it first followed by their first name, separated by a period, which is unique. It's written as follows: M. Sukumar
Now the question is, how to write the expanded (full) name, whenever requested. The universally accepted order is: First + Last, as follows: Sukumar Michael, unless you're asked to state your last name first.
In the West, on some official documents or ID's such as a driver's licence, there's a practice of stating the last name first, followed by the first. In such cases, the full name is written as follows: Michael, Sukumar. - Here, the comma right next to Michael indicates that it's the last name. Not to worry. It's generally understood by the officials, although, I must admit, confusing for the individuals themselves.