Formal:
* Je m'appelle Connor. (This is the most common and neutral way to say it.)
Informal:
* Je suis Connor. (This is more informal and translates literally to "I am Connor.")
More informal:
* C'est Connor. (This is very informal and translates literally to "It's Connor.")
You can also use the name "Connor" directly in a sentence:
* Connor, c'est moi. (This translates to "Connor, it's me.")
The best way to choose the right phrase depends on the situation and your relationship with the person you're talking to.