If the phone rings and it's not a friend of yours, then most people in Germany answer by saying their last name. You can also say your first and last name, as well as a greeting, like this:
Claudia Schmitt, hallo?
In a professional situation, you say the name of your company first:
Deutsche Welle, Schmitt, guten Tag.
Firma XY, ja bitte?
During a formal telephone call, you also normally say your name:
Hier ist Schmitt, hallo.
Claudia Schmitt, kann ich bitte …
Particularly in a formal context, it is considered impolite not to say your name.
Then, a person will often ask you:
Mit wem spreche ich, bitte?
Wie war nochmal Ihr Name?
- Ah, entschuldigen Sie, mein Name ist Carlos Fischer.
On the phone, there is also a particular way of saying goodbye:
But you can also say "Auf Wiedersehen" or "Tschüss".
Talking on the phone in a foreign language is quite difficult because you cannot see the other person's facial expressions or body language. If you haven't fully understood something, it's a good idea to ask them to repeat themselves.