The two conditions attached to Pip's great expectations are:
1. That he must always keep the name of Pip.
2. That he must never try to find out the name of his benefactor. Mr. Jaggers tells him:
"Now, you are distinctly to understand that you are most positively prohibited from making any inquiry on this head, or any allusion or reference, however distant, to any individual whomsoever as the individual, in all the communications you may have with me."
It must seem strange to Pip that he should be required to keep that name rather than Pirrip, since he naturally assumes that his benefactor is Miss Havisham and that she knows him very well and will always be able to contact him. But the real benefactor, Abel Magwitch, is in New South Wales and wants to be sure of being able to find Pip if and when he returns to England. Pip is a very unique name. Magwitch should have no trouble finding a man bearing such a name. He knows, of course, that Pip will have grown and changed considerably, so it would be difficult for Magwitch to find him years later on the basis of his appearance. Besides that, Pip will have become a "gentleman." If Pip thinks about this condition he must put it down as just one of Miss Havisham's many eccentricities. But he may also regard it as a sign of her secret affection for him, a matter of prime importance. She could only be doing this for him because she has developed a great fondness for him.
As far as the second condition is concerned, why does Magwitch wish to remain anonymous and act only through Mr. Jaggers? It is this anonymity that causes many of Pip's troubles. The answer must be related to the first condition. Jaggers intends to return to England someday, knowing full well that it is a capital offense. He therefore believes it is better that Pip should not know his benefactor is a transported convict living in New South Wales, because Pip could talk too much and let the wrong people know that Magwitch is planning to violate the law and risk losing all his money by returning to England. Pip, however, thinks it is Miss Havisham who wishes to remain anonymous, and he probably surmises that she wants to keep her generosity a strict secret from her greedy relatives. If the relatives we have met suspected they were in danger of losing Miss Havisham's entire fortune upon her death, they might decide to take legal action to have her declared mentally incompetent so that they could become joint custodians and conservators of her estate. In other words, Pip probably secretly believes that the old woman is going to leave him all her money and wants him to marry Estella. He believes this because he is madly in love with Estella and wants to believe it. People tend to believe what they want to believe. And furthermore, it never occurs to Pip that there could be any other rich benefactor than Miss Havisham. She is the only rich person he knows. Magwitch certainly does not seem to have much potential for getting rich when Pip meets him on the marshes.
Jaggers has his hand in framing this second condition. He would prefer not to have it known that he is representing a transported convict in Australia because, for one thing, it would suggest that he knows Magwitch is planning to return to England in flagrant violation of the law. It is probably Jaggers rather than Magwitch who spells out that second condition of strict secrecy about the identity of Pip's benefactor.
Pip is in a funny position. He is an affluent London gentleman of leisure, but he has no sense of security whatsoever. He is only prepared to be a useless gentleman and has no trade or profession to fall back on if his allowance were to stop coming. It is bad enough to be dependent on another person's good will, but it is much worse to be dependent on the good will of a person who is unknown and invisible.