We first learn Victor Frankenstein's full name at the beginning of Chapter 5, when he receives a letter addressed to him from Elizabeth Lavenza, his cousin and future (intended) wife.
I think there are a number of possible reasons for this delay:
First, not knowing someone's name is very alienating. Our names feel integral to our identities and so refusing to call someone by their name is ultimately dehumanizing. Perhaps Shelley is commenting on Victor's apparent lack of humanity by refusing to name him for so long. Such a move draws further attention to the way in which his "human nature turn[ed] with loathing from [his] occupation" when he was digging up bodies and visiting morgues in order to supply himself with parts for his experiment.
Second, she might also refuse to name him to point out the inhumane way he treats his "creature" once it comes to life. After having stared at this creature for months on end, in witnessing him come to life, Victor says that "no mortal could support the horror of [his creature's] countenance," literally placing himself outside the realm of humans (who would not have been able to handle it). Simply abandoning his creature to the elements is both cruel and ultimately traumatizing to the creature himself.
Third, Victor never names the person he makes (another way in which he dehumanizes his creation), and Shelley goes to great lengths later in the novel to show readers just how similar Victor and his creature really are: starting with good intentions, wanting to help humanity, etc. Not naming him until later places readers in the same position regarding his namelessness as we are when it comes to the creature. It's just one more way in which they are so alike (both are monstrous and both are good -- this duality is key to human nature in this book).