Minun/Mun nimeni/nimi on...
I'm wondering what is the most natural way to say ''My name is...'

I think all of these options are correct:
Minun nimeni on...
Mun nimeni on...
Minun nimi on...
Mun nimi on...
Nimeni on...

Am I right?
Which one you will use if you meet a person about your age somewhere in a club and want to introduce yourself? Which one seems to be most common? Or maybe the best option would be "Olen..." like "I'm..." in English?

Question

Minun/Mun nimeni/nimi on...
I'm wondering what is the most natural way to say ''My name is...'

I think all of these options are correct:
Minun nimeni on...
Mun nimeni on...
Minun nimi on...
Mun nimi on...
Nimeni on...

Am I right? 
Which one you will use if you meet a person about your age somewhere in a club and want to introduce yourself? Which one seems to be most common? Or maybe the best option would be "Olen..." like "I'm..." in English?

Answer

Most natural way to say ''My name is...'
It really depends on the situation. in a unformal situation like at club or bar I would not use "Nimeni" at all.
probably would use something short like:"Vilho" terve. or Mä oon "Vilho" Where "mä" is sort for "minä".

Answer

I agree with the others, "mä oon..." is maybe the most natural in an unofficial situations. All the examples are correct though! "mun nimi on..." would be the one I would use most (after "mä oon...").

Answer

When I meet someone I haven't met before the most natural way to introduce myself would be "Moro! Mä oon Fritz".

"Moro" is colloquial for "hello" or "hi". You can switch it with "hei", "moi", "moikka" and so on...

Answer

Finns can sometimes be quite strange, and I would not be surprised if they would say nothing but their name, for example: "Matti."