It's a silly nitpick anyway. The monster, Adam, calls the doctor, Victor Frankenstein, his father. Surnames are inherited, thus they are both Frankensteins.
No it isn't. He compares himself to Adam once ("I ought to be thy Adam, but I am rather the fallen angel, whom thou drivest from joy for no misdeed") but he never calls himself that. And frankly, considering how much Frankenstein and the monster hated each other I don't think either of them would want to share a name.
Slavoj Žižek's Freudian-Hegelian interpretation of Mary Shelley's story is worth investigating especially in relation to Shelley's family, the French Revolution, and transgressive sexual politics.