I'm still not convinced if "it" really refers to the person (it seems strange to refer to a human as "it"), or their name. "It (your name) is Ariadne, isn't it?" This is an indirect form often found in formal and business English, ie. talk about an "outside thing" instead of direct address. "Are you Ariadne?" seems as if you were looking for someone named Ariadne, or if you just realised the Ariadne you'd heard of is standing in front of you ("Oh! Are YOU Ariadne?") "You are Ariadne, aren't you?" means I think your name is Ariadne and just want you to confirm. The directness itself isn't exceptionally rude, but there are good suggestions above for using direct address with politeness.

In this case, the third person of singular - "it" -, doesn't have much to do with politeness. The pronoun is only substituting the subject. It can be replaced by: YOUR NAME (subject) is Adriane, isn't it?

All of the examples are grammatically correct and appropriate. None of them are particularly formal. As to rudeness, I think that depends on the culture or environment from which the recipient comes. In a party setting, or for that matter any other setting that is not very formal, Are you Ariadne? sounds the "rudest" because it does not seem to have any "softness" to it. The other two expressions have words that seem to be more apologetic. To soften this one, you might say, "Excuse me, but are you Ariadne?" or even better, "Excuse me, but is your name Ariadne?".

Olga, I hope you don't come away with the impression that English speakers will give you the cold shoulder if you happen to use a narrative form that isn't perfectly suited to the situation. In real life, communication tends to be quite informal - I can definitely say that for Americans anyway. And whatever formality might exist quickly dissipates if I hear a non-native speaker (meaning that they have an accent) speaking English. In other words, I'm concerned even less about narrative forms.

actually, using the third person in your example is more CASUAL. it makes sense at a party setting, but it is not appropriate for formal or written English.