I usually tell them who I am and then ask for the person I need. Since I'm usually only calling my own users, they already know who I am from my name or at least when I say I'm from the Computer Center.
I believe it's courtesy to introduce yourself before you ask for someone else.
So, I would say something like,
"Good morning, this is Dennis from Computer Tek. I need to speak to John about the repair of his computer if he is available?"