Why do you think it is one of Magwitch's principal conditions that Pip "always bear the name Pip" in order to receive his financial support?
It is in Chapter 18 that Jaggers arrives and tells Pip of his "Great Expectations" and the money that he has. It is also where Jaggers explains the conditions of accepting this money: to "always bear the name of Pip" and to never enquire as to the identity of his benefactor. It is in Chapter 39 where Magwitch declares himself and we begin to understand something of the complex motivations behind Magwitch's motives for "owning a London gentleman". Although it is never explicitly stated, perhaps we can infer that Magwitch wanted Pip to keep his name as a reminder of his humble origins, to flaunt how far he has risen in society and therefore reinforce Magwitch's pleasure of having created a gentleman through his wealth, despite his background.
This of course ties in to one of the key themes of the novel - what is a gentleman and how is one created. Of course, the novel suggests that no matter how much wealth you have, it takes more than "portable property" to be a true gentleman - as the frequent contrasts between Joe and Pip establish.