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:

Schmitt?

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:

Auf Wiederhören.

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.