The interaction between Pip and Jaggers develops the conflict in the story because Pip's dream of a grand fortune is suddenly challenged by the condition of retaining his current name.
How the conflict is developed
Jaggers' vague threats about removing Pip if he objects create an atmosphere of fear and uncertainty as Pip is now forced to make a difficult choice that could impact his future.
Also, the offer of "great expectations" fuels Pip's ambition but also exposes his insecurity about his social standing. Jaggers' presence forces him to confront his conflicting desires for belonging to his current life and escaping his poverty.