The drug Molly gave Sherlock in order to help him fake his death turns him into a child. He retains the mind of an adult, but has the body of a ten year old. Nobody knows if Moriarty survived and his gang is still active, therefore he deems it too dangerous to tell everyone the truth, just Molly and Mycroft finds it out on his own. Since his notes are all at 221B Baker Street, he moves in with John and pretends to be a child. John adopts him, because he reminds him so much of Sherlock. He calls himself Conan creates this secret identity his secret identity in order to hunt down Moriarty's Organization and find that bloody antidote because he can't stand seeing John slip more and more into depression.
( This prompt has been heavily inspired by Detective Conan)