You could introduce yourself by saying "Hi, I'm Lynn. I'm a Product Manager with XYZ company". They will usually introduce themselves to you the same way. Of course replace Product Manager and XYZ company with what you really do for work. If the other person only gives you their name, it is acceptable to ask what company they work for. If you know who they work for already, you can ask what their role is in the company.

Just for reassurance, Jeremy's answer is right. Always start by introducing yourself, not by just asking the other person, which would be seen as rude.

the polite way to ask some one name is would u like to introduce yourself