Such a cutie. We have a female sun conure named Milo (adopted with this name). As far as names, it depends on which direction do you want to head in. I have always personally thought that sun conures with their bright colors remind me of a basket of fruit so I like names like Mango, Kiwi, or Tangie (like tangerine). You could also go for "sun" type names for sun conure such as Sunny or Kaoli (morning glory in hawaiian). You could even go with names like Tiki, Hoku, or Manu which are more Hawaiian type names. Or my last suggestion would be Phoenix because my husband always says when Milo gets wet he looks like he's on fire with his bright colors.
We personally don't mind the loud screams but working in the rescue 24/7 (LOL!) we get used to it! Some people though buy them and then notice their loud screams and can't deal with it. Like Milo's previous owner and Mango and Tangie who were both in the rescue.