Skywalker, however, was the name Luke knew his entire life. He didn’t know the whole truth about his father, but he knew his father was a hero at one time. And he was raised by people who were connected as family to his father (even if they did have a different name).
Rey, on the other hand, grew up with no family and no name. She knew her blood family’s name for all of 5 minutes and knew Palpatine as the name of the most evil and despised man in the galaxy. It wasn’t a name that she ever had any real connection with. Her family (adopted or not) was Luke, Leia, Han, even Ben. So why not take that family name as her own?