This study investigates the perceptions of students and employees at a German university regarding their institution's customized Large Language Model as-a-Service (LLMaaS) chatbot compared to the widely used commercial chatbot, ChatGPT. Conducted with a sample of 526 participants, the research employs a survey-based field study to explore user trust, privacy concerns, and experiences with both chatbots. Key findings reveal that users reported significantly greater trust, higher perceived privacy, and fewer hallucinations when interacting with the university's customized LLMaaS chatbot compared to ChatGPT. These results suggest that user-facing customizations play a crucial role in shaping perceptions and behaviors towards LLM chatbots. The study draws on the Trustworthiness Assessment Model (TrAM) to theorize that these customizations serve as cues influencing users' trustworthiness assessments. The implications of these findings extend to the design and deployment of LLMaaS chatbots, providing organizations with practical recommendations for enhancing user engagement and ensuring informed, secure, and sustainable use of AI technologies in educational settings.