Final answer:
The real name of the boy Sophie thought of as Weasel Boy is Annie P. Miller.
Step-by-step explanation:
The real name of the boy Sophie thought of as Weasel Boy is Annie P. Miller. In the text, it is mentioned that Sophie's real name is not Daisy Miller, the name she goes by on her cards. Her brother reveals that her actual name is Annie P. Miller. This information suggests that when Sophie mistakenly thought of the boy as the Weasel Boy, she was actually thinking of her brother Annie P. Miller.