I am sorry, I read your question wrong. I thought you were asking for ways to answer the phone, but you could also be asking about how to introduce yourself when you are the one making the call.
If you are calling someone on the phone you normally say: "Hello, this is Mike Surname calling" or "Hello, my name is Mike Surname." Again, it will depend on the person you are calling.
Of course you will not need to give your full name when you are calling a close friend, but when it comes to professional relationships and strangers you should always be polite and introduce yourself clearly.