I would say the second phrase is slightly less derogatory.

The reason is the first question seems to me more rhetorical and insulting. It sounds like just a soften version of Qu’est-ce [que] ça peut te foutre ?

No answer is really expected because someone’s name cannot faire (or foutre) anything to anyone.

The second sentence shows more contempt but is leaving a slight opportunity for the other person to answer and explain his/her interest in the speaker’s name.

Of course, the tone used and the context matters a lot.

Both are addressing directly the listener (through the use of vous) and should be perceived as a message to them that their curiosity is not welcome. They are both somewhat rude, but quite possibly because of an inquisitiveness that was considered rude in the first place.

Rating them, this answer cautiously states the second one would be less derogatory than the first. My own vision of the thing would lean somewhat, feebly, on the opposite side. So I believe it is a matter of opinion with no absolute good answer.

A milder version of both, though still clear and unambiguous enough, could be:

• Je ne vois pas en quoi ça vous intéresse.

It is softer a bit in the sense that it’s not asking a question that is not meant to be answered, but rather simply stating a fact.

On the whole the nuances depends on the context and the tone ; the two formulations can be used in a heated argument or, especially the first one, be the mark of an abrupt change in the relationship between the interlocutors.

“En quoi ça vous regarde ?” can be used in place of the “Qu’est-ce que ça peut vous faire ?” with the same effect on condition the tone affected in saying it be full of contempt and reprobatory enough ; otherwise it can be an utterance quite short of the expected aim, this aim being to show to someone that they went way beyond the limits of polite behaviour, that they behaved in a disrespecful manner and that you are not only mad at them but that from now on you despise them. The first utterance and the second one, that latter properly delivered, are enough to signal to someone a rupture in normal relations.

The second formulation can however be a very matter of fact question, although a variety of nuances are possible, those connoting a certain joviality and those not so nice in their undertones. It must be said that the first formulation can also be used in a subdued manner, without being as mean as is usually the case when using it. In a dialogue in which the speakers are endowed with enough resilience it can be managed without dramatic conséquences but things turn out are rather rarely that way, the result being most often for one to whom were intended those words the feeling that they’ve been meted out a severe punishment, so much so that sometimes they’ll recognize having misbehaved and apologize. It’s better to use the first one only in those cases when has been felt disrespect and that there is a need to remind the offender to keep their distance.

If it’s interrogative, no harm.

But most of the time it will sound really defiant / agressive depending..

In your sentences ‘ouais’ seems to set the tone for the second option… I think I’d receive your words unpleasantly. If you want to reject the other person, you can use that tone. Otherwise the simplest is to ask “Pourquoi ?”.