I am / I'm Ishikawa...

My name is . . . would be better.

"I'm John" sounds foreign or something a small child would say to introduce themselves.

Thanks, Punkey.

I'm surprised because I thought when it is a speech, the short forms should be used, that is, I'm instead of I am.

Well, speech patterns say something about the character.

"My name is" indicates someone who knows the difference between a thing and its label.

"I am" indicates someone either formal or very deliberate and measured in their delivery.

"I'm" indicates someone informal or perhaps with a very quick speech pattern.

I would use the I am / I'm formulation if I was introducing myself as part of a group of people.

This is Diane, this is Debra, this is John and I'm Beth.

or if several people are introducing themselves - i.e. in a class setting

If Í was only introducing myself, I'd be more likely to say, My name is Beth.