A robot's personality can shape user experience and acceptance in many social robot applications. Allowing users to customize robot personality could help them tailor robot products to their preferences, but it remains unclear whether this customization diminishes perceptions of the robot as a social agent and whether robot form factor influences these effects. We conducted a 2x2 between-subjects study (N = 79) examining robot form factor (humanoid NAO vs. non-humanoid TurtleBot) and personality customizability (customizable vs. non-customizable) during a collaborative event-planning task. Our results reveal that while customization reduced perceived social agency for both robot types, this reduction was particularly evident for humanoid robots. Conversely, personality customization significantly improved human-robot rapport, with this improvement driven primarily by non-humanoid robots. These findings reveal form factor-dependent effects in personality customization, indicating that robot form and customization capabilities yield differential impacts on perceived social agency and human-robot rapport in human-robot interaction design.