In my experience, this is context-dependent. In person in a small group, you'd say "Hi! I'm James!" and probably extend your hand to shake. This is also what you'd do if you're in front of a room introducing yourself — "My name is James" would also work there, especially if you're not the main speaker in a talk or something.
However, if you're joining a conference call, where you expect people know who you are but as a courtesy because you don't necessarily expect them to be able to distinguish your voice, you'd say "Hi! This is James."
In the second situation, the people who you are introducing yourself to know what your name is; they just don't know that this voice is you.
And, you might do the same even if there's video, for people who might not be getting the video or similar.