Large language models (LLMs) are widely used for personalized tasks involving sensitive information, raising privacy concerns. While anonymization techniques exist, their impact on response quality remains underexplored. This paper introduces a fully automated evaluation framework to assess anonymization strategies in LLM-generated responses. We generate synthetic prompts for three personal tasks—personal introductions, cover letters, and email writing—and apply anonymization techniques that preserve fluency while enabling entity backmapping. We test three anonymization strategies: simple masking, adding context to masked entities, and pseudonymization. Results show minimal response quality loss (roughly 1 point on a 10-point scale) while achieving 97%-99% entity masking. Responses generated with Llama 3.3:70b perform best with simple entity masking, while GPT-4o benefits from contextual cues. This study provides a framework and empirical insights into balancing privacy protection and response quality in LLM applications.