What's happening here is that your employer has an institutional contract with Microsoft to give you access to Copilot. If your name and role are used, it's because those are considered part of institutional knowledge as part of your Microsoft account. Alongside the contract, there is a data processing agreement which controls where that information can be shared - which is usually only within the institution. The agreement should also say that your name/ID are unlinked from the queries you make, so cannot be sent outside the university (since the ID needs to be linked back to the response Copilot makes, you have to wonder if it is actually possible to recreate that link), and also that your queries will not be used for future Large Language Model training.
Some types of Copilot contract also allow Copilot access to all of your Microsoft managed files: Outlook for email, OneDrive for documents, OneNote for notes, and so on. You should know if you have this access, since it costs extra and someone will have checked up whether you want it. So a question to Copilot might bring a response which references files you have saved. If you are wondering why anyone would want this, it could be useful for helping you to pull together relevant information. Requests like "list all the files which are related to X project" might bring up some (ahem) misfiled items or meeting notes you have forgotten, or help you combine information from different types of files (Excel and Powerpoint, for instance). But if you have this option and find it creepy, ask someone to cancel your subscription: every little helps the university budget! Whilst personal information you hold in a limited way for the purposes of your job should be secure within this kind of data agreement, you can move files you definitely don't want the GenAI product to have access to into a different location which Copilot does not have access to (e.g. the hard drive of your computer). If you aren't sure what is allowed, check with your organisation's data controller.
It's worth noting that this is a question where digital inequalities rear their heads, alongside very reasonable concerns about data privacy. Students may not have access to this 'safe' way of using a GenAI product with a reliable data processing agreement. Just using the free versions of products may put them at risk of their chats being exposed in security breaches, used for training, and they may, intentionally or not, also be sharing copyright, personal or sensitive data more widely by uploading to a GenAI product. They may also not have access to the most recent version of the products, but that isn't the focus of your question.