So the only way to solve this question is by process of elimination.
Let us start with first names that have 5 letters:
Simon’s and Dylan’s surnames cannot be Doyle, Floyd or Shore since the first name and the second name cannot contain the same number of letters. The only remaining surnames are Hyde and Rush.
Dylan’s surname cannot be Hyde as the letter ‘y’ is repeated. So Dylan’s surname would be Rush.
Hence, Simon’s surname is Hyde.
Boys with first names that have 4 letters:
Liam’s surname cannot be Doyle or Floyd as they contain the letter ‘L’. So Liam’s surname must be Shore.
Eric’s surname cannot be Doyle as it contains the letter ‘e’. So Eric’s surname must be Floyd.
The only remaining surname is Doyle. The answer is A.