Formal or Business
Caller: Hello, (whether you should identify yourself at this point depends upon many factors) may I speak to John Smith please?
Responder: This is John.
Caller: Hi Mr Snow. Is Sue there?
Caller: Hi Mr Snow, this is John (or John Smith). Is Sue there? (Whether it's necessary to identify yourself depends upon the age of Sue, whether or not Mr Snow is likely to recognize your voice and how well you know Sue)
Caller: Hello, my name is John Smith. Can I interest you today in a very special deal on widget insurance?
Responder (Sue): Hello?
Caller: Hey Sue, it's John. Do we have a date tonight?
Especially for business calls, you probably want to use your whole name to introduce yourself to someone you have never spoken with before. Alternatively, you can say "Hello, this is John from Widget Fidelity. May I speak to Sue Snow please?"
This is a pet peeve of mine, so please, please, PLEASE - If you made the call, never ask who you are speaking to before you identify yourself.
Finally, if someone calls (business or personal) and you answer the phone for somebody else, you may feel the need to identify the caller for the recipient. If so, say, "May I ask who's calling?"