Dr. Frankenstein gave the monster life. Therefore, it should get his last name.

Part of Frankenstein’s rejection of his creation is the fact that he does not give him a name. Instead, Frankenstein’s creation is referred to by words such as “wretch”, “monster”, “creature”, “demon”, “devil”, “fiend”, and “it”. When Frankenstein converses with the creature, he addresses him as “vile insect”, “abhorred monster”, “fiend”, “wretched devil”, and “abhorred devil”.

And Victor should keep the interpretational sovereignty?

Why would monster want to take on that name?