It is quite difficult to say without much context, but 'to ask for someone' can have a wide range of meanings. It generally means to ask to speak to someone, to get someone's attention, or to book an appointment with someone. In fact, both situations that you have written are possible, but more context would give you a better idea.
Other examples include:
'The customer is asking for the manager' - The customer wants to speak to the manager
At the hairdressers: 'The customer was asking for John, but I told him that John is ill at the moment.' - The customer wanted to book an appointment with John, but he is ill at the moment
You can also 'ask for someone to do something'
'She was asking for her daughter to come home' - She was asking someone (not her daughter directly) to tell her daughter to come home. This would be situation 2 in your explanation.
I hope this helps!