The difference lies in the stress of both words. онá or Áнна
"Анна" has a stress on the first syllable, and "она" on the second one.
The pronounciation of these words is different: "она" - "ана́" and "Анна" - "А́н-на". So, "Анна" has double "n" in its pronounciation.
There were plenty of surnames they could have picked, yet they've decided to choose the one which was more likely to cause confusions. Well...
Does this mean that she wants to live a virtuous life? Or that she wants to live in luxury?
Luxury. You also can say this in Russian another way "она́ хо́чет хорошо́ жить" ="she wants to live well"
Because the accusative form of жизнь stays the same, and here that is the case.
Is it хорошую because she wants the life for herself, or for some other reason?