"Einen habe ich Ihnen bereits genannt."
tell them, not us. If you speak English, you know that named and called are synonyms.
Yes, but not necessarily in this context. In this context "called" would be more like "aufrufen"
In this context, called would mean made a phone call. As in, "I need a taxi" "Don't worry, I've already called one for you". But note that even here it's not "I already called you one".
"Called" is just not an appropriate translation for genannt in this context (whereas in other contexts it clearly is)