I think you are jumping to conclusions, but in most cases I think you are right. It's our language, we just know, but we don't know, you know?
If a word starts with G it almost always stays a G. The names Gustav and Gabriel aren't pronounced Justav or Jabriel lol. Then there are other instances where the "G" becomes a sch-sound, just as in the english language. The 2nd G in "Garage" for example.
Swedish is a close relative to English, and so many words are similar. But our grammatic rules are often inconsistant, as you will see in this comedic video:
Right in the beginning of the video, the host says the letters Å, Ä and Ö. So right there is how you start Åbergs name