While existing spoken dialogue systems can adapt various aspects of interaction, systematic management of psychological distance through verbal politeness remains underexplored. Current approaches typically maintain fixed levels of formality and social distance, limiting naturalness in long-term human-agent interactions. We propose a novel dialogue management model that dynamically adjusts verbal politeness levels in Japanese based on user preferences. We evaluated the model using two pseudo-users with distinct distance preferences in daily conversations. Human observers (n=20) assessed the interactions, with 70% successfully distinguishing the intended social distance variations. The results demonstrate that systematic modulation of verbal politeness can create perceptibly different levels of psychological distance in spoken dialogue, with implications for culturally appropriate human-agent interaction in Japanese contexts.