The idea that his father wouldn't want to hurt the Doctor was confusing, but Samuel tried his best to understand it. All of this about other universes and people not being who they were was a lot for his little brain to process. If anything he was willing to accept things as they were told to him because he was too tired to do much else. So sure, his father and the Doctor somewhere else were best friends.
"Oh," he said sheepishly. He wiped a hand hastily on his trouser leg and offered it formally to the Doctor. "I'm Samuel. Saxon. Samuel Saxon," he answered. "Sorry."