A chat with your logo on your own domain feels like an internal environment. It says little about where questions and documents are processed. That depends on the components connected behind the interface.
The interface and model are separate
Open WebUI is one example of a chat environment you can manage yourself. Its documentation describes connections to Ollama and external model providers. Your own interface can therefore rely on a model running elsewhere.
Document processing, web searches and other features may introduce additional connections. Checking where the website runs is not enough.
Follow the path of one question
Imagine an employee asking about an internal manual. Where is the file stored? Which component retrieves relevant passages? Where is the answer generated? What remains in chat history and logs?
I would map one example first. That makes privacy and management discussions concrete. The diagram need not be complex: it should show where information goes.
Local hosting still needs maintenance
A local model may suit information that must remain in your own environment. You still need to assess hardware capacity and answer quality, and arrange access controls, updates and backups.
Open WebUI’s guide notes that conversations, users and settings need persistent storage. Someone must take responsibility for this information, even in a small trial.
Start with a shared-access collection
For an initial test, choose a small user group and a limited document collection. Agree who may access it and test questions the documents do not answer.
A privacy-conscious setup depends on choices throughout the processing chain. I would document those choices before installing the chat environment.
Sources and further reading
Explanation and commentary based on the sources below. Examples are illustrative.