Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
You can only change things you don’t know about in advance. You know Hitler became chancellor of Germany, so you can’t change that. But you can change the name of his dogs if you don’t know what they were, and nobody who knew sent you back in time.
What if you tried to change his dog’s name to something very unlikely? Like, I’m really pretty sure Hitler’s dog wasn’t named Bark Obama, but I really cannot be 100% sure.
If the fact that President Obama didn’t share a name with one of Hitler’s dogs was historically impactful enough to shape your decision to go back in time and change the dog’s name, then you can’t do it.
If there’s a possible way that the dog could have had that name and you wouldn’t have been aware of it (like if the media never connected the dots), then it’s possible.