This question is one that the text does not answer, and so it is up to us as keen, intelligent readers to try and infer the reason behind this somewhat odd request of Magwitch. It is important to focus on the reasons why Magwitch wanted to make Pip into a gentleman, when he first appears to Pip and reveals his position as Pip's mystery benefactor:
"And then, dear boy, it was a recompense to me, look'ee here, to know in secret that I was making a gentleman. The blood horses of them colonists might fling up the dust over me as I was walking; what do I say? I says to myself, 'I'm making a better gentleman nor ever you'll be!' When one of 'em says to another, 'He was a convict, a few years ago, and is a ignorant common fellow now, for all he's lucky,' what do I say? I says to myself, 'If I ain't a gentleman, nor yet ain't got no learning, I'm the owner of such. All on you owns stock and land; which on you owns a brought-up London gentleman?'"
It is well worth analysing this in detail - Magwitch seems to want to "own" a gentleman primarily as a way of getting back at a class system to which he is always excluded and rejected. He takes great delight in being able to consider himself superior to the colonists because he "owns" someone who is better and more cultured than they will ever be, and seems to be satisfied to enjoy vicariously the position in society that Pip is able to command because of his patronage. Thus, retaining the simple name Pip, maybe a symbol of just how much Magwitch rejects the social norms that have ostracised him.
However, consider the name "Pip" and why Dickens chose to use it. This novel is known as a bildungsroman, in that it focuses on the education and development of one central character and charts their transformation from childhood to becoming a useful member of society. Thus the name "Pip" emphasises this theme by comparing Pip to a seed that has been planted and is being nurtured in different ways. We as readers are keen to know how this Pip is going to grow and develop, and what kind of plant will finally emerge.
Other than reader conjectures, there are some indications in the narrative of Great Expectations that point to possible reasons for Magwitch's insisting that Pip retain his childhood name:
- If Pip changes his name, it will be difficult for Magwitch to find him if he gets out of prison or escapes and wishes to see Pip. When Magwitch does appear on the stairs of Pip's apartment at Barnyard's Inn, obviously he has somehow obtained knowledge of Pip's whereabouts from someone. If Pip goes by another name, Magwitch can have no way of knowing what this name is.
- By Pip's retaining his name, news of him would be discussed at the Boar's Inn where prisoners are placed on the coach. For instance, in one chapter, as Pip rides to Miss Havisham's, he overhears two prisoners talking about Magwitch's having given one some money to give the boy. This convict is the one who held the file and stirred it one night when little Pip was with Joe at the Boar's Inn. So, Magwitch can learn from the prison "grapevine" about Pip if he retains the same name. This is probably how he has found Pip in London.
Pip is a childish name. Magwitch's fondest memory of Pip occurred when Pip stole and lied for him. Magwitch wants to forever hold this memory and return the favor in some way. Nothing else good has happened in his life except for this one moment when someone else sacrificed themselves for him.
Even though Magwitch wants to help him become something more, I think he wants to make sure that Pip hangs onto his identity and what simple roots he came from. He would hate to see Pip change to be someone like Compeyson and deal rudely with people left and right. It's interesting that a convict would have such profound morals or virtues, but Magwitch certainly does.
In my opinion, this is because Magwitch wants Pip to change, but he does not want Pip to change in the most important ways.
Obviously, Magwitch wants to remake Pip's life. He wants to give Pip opportunities -- to give him a chance at a better life. But at the same time, he thinks that Pip is a good person and he does not want him to change. He wants Pip to remain the same person that he is at the point when they meet. I think that he wants Pip to keep that name so that Pip does not forget who he really is.
We can see that Pip has problems doing this over the course of the book, but in the end he becomes pretty much the same good person he was at first.
For obviously practical reasons of identification.
Once Magwitch has been arrested and sent to exile in Australia he works hard and tirelessly to somehow repay the kindness that Pip and no one else had shown him throughout his life and to transform Pip into a "gentleman" and thus take his revenge on the crooked penal system which judges only by appearance and circumstantial evidence and not by evidence based on facts.
Australia was miles and miles away from England and separated by two oceans. It was accepted that once a person was sent off to Australia there was no chance of seeing him again. The only means of communication would have been by couriers who would have acted on trust or by means of a personal agent like Jaggers.
Magwitch insists that Pip does not change his name so that he could regularly send money to him in faraway England and that the money would safely reach him and only him and no one else