[Though Leia glances at the tea as Qui-Gon pours them both a cup, she makes no move to reach for it. Were it a more pleasant conversation, she would, but discussing Darth Vader is about as far from that as it's possible to be. The main reason she decides against reaching for it is because she's unsure what sort of reaction it might have, thanks to Verens' unique environment. Something worth noting, especially since despite Leia's best efforts and though her outward appearance does not change much, the temperature in the room rises a few degrees as soon as Qui-Gon describes Anakin as her father.]

I claim no relation to Anakin Skywalker, and I'd like it if you respected that.

[the tone used to say Anakin's name implies she 100% means that as Darth Vader. She knows she's related to him, of course, as much as she hates it, but she doesn't have to acknowledge it beyond that as far as she's concerned. She would prefer it stay a secret no one else in the galaxy knows, even though by now she knows better.]

The man I consider my father is the man who cared for me and raised me as his own, not the monster who forced me to watch my planet's final moments.

[it's not as if she wants to talk about Alderaan, but since it no doubt will be heading there anyway, it's best to get it out of the way now. She's mostly hoping it has the added effect of ensuring Qui-Gon not call Anakin her father. At least, not where she can hear it anyway.]