When I studied at the university, here, in Ukraine, in the late 90s, our professor of English and American literature was outraged by that spelling, and even in our examination cards in his subject he spelled "Bernard Shaw" as "Бернард Шо". Moreover, he also spelled "Edgar Poe" as "Эдгар Поу", although the standard Russian rendering of that name is "Эдгар По". < we had a joke that the two writers, Shaw and Poe, were mirror spelling twins :D >
I am sure, that the Шоу spelling is just a result of a historical accident. Since the 19th century several ways of rendering of the English names were used, almost every quarter of a century they changed, creating lots of variants of the same English name. For example, "William" is Вильям, but also Уильям. The famous biologist Thomas Henry Huxley is Гексли, but his grandson, a famous writer Aldous Leonard Huxley, is Хаксли. James used to be Джемс, but now it is almost always Джеймс.
There is also a long tradition of rendering the names of the English and British monarchs not the way they sound in English, but in their Latin form adapted to Russian phonetics and morphology:
- Alfred is Альфрéд
- Harold is Гарóльд
- Henry is Гéнрих
- John is Иоáнн
- Charles is Карл
- James is Яков or Иáков
- Mary is Мария
- Louis is Людóвик
- Stephen is Стефáн
- Anne is Áнна
- George is Геóрг
- Edward is Эдуáрд
- Elizabeth is Елизавéта
The point is, when it goes about the names of celebrities, one has to know exactly how the person's name is rendered in Russian. There is no set of rules you can use to render those names yourself. The easiest way is to find the Wiki article about the person and then switch it to Russian, but still, you should be ready to see several Russian variants of the person's name there.
