To introduce yourself in English, you can follow the following patterns:

Hi (greeting)

I’m _______ (name).

Allow the other person to introduce himself / herself.

Follow up with:

Nice to meet you, (repeat the other person’s name). 

For example,

1. I’m John.

I’m Jackie.   (Use first name in informal situations)

2. I’m John Kennedy.

I’m Jackie O’Neill.    (Use full name in business and formal situations)

3. (It’s) nice to meet you.

(It’s) nice meeting you.     (It’s) good to meet you.

4. It’s nice to meet you too, Jackie.

5. Nice to meet you too, John.