Hív is 'to call'. (Well, technically it's 'he/she/it calls' since the dictionary entries always refer to the third person singular form of the verb; the infinitive 'to call' is hívni )
And the suffix -nak conjugates it into the third person plural: they call.
"How are they calling?" Hogy - how; hívnak - they call. In this case, how they are calling you. Note that there isn't a passive voice in Hungarian. Using 'they' as the active part is one of the workarounds that is frequently used.
There is no difference, both can be used in formal situations. At least in the company where you can address people by their first name: among young people, for instance. In other cases it is better to ask "Önt hogy hívják?" or "Önnek mi a neve?"