Chats yes, Pages no. Put a naming rule in your custom instructions or save it as a memory, and new chats then follow it in your chat history. Pages are different: Copilot names them in a premade way before it reads your instructions, so rename each page yourself into whatever structure you want.
More in Microsoft Copilot
What is the Library in Copilot?
The Library, in Copilot's left-hand bar, is where Copilot stores what it creates: your Pages, canvases, generated images and other creations. It is storage, not a working feature, and it does not run prompts. Pages are saved there automatically, and a page survives even if you delete the chat it came from.
Can my colleagues or IT see my Microsoft Copilot chats?
Your colleagues cannot see your Copilot chats. Microsoft 365 Copilot only works inside your own permissions, so nobody can ask it about your mail or files. Your organisation can still keep and search Copilot conversations for compliance and audit through Microsoft Purview, the same way it can with email, so treat work chats as work records.
Does Microsoft Copilot warn me if I paste Personal Data?
Not reliably, so do not depend on it. Some organisations set up data loss prevention policies that can block or flag sensitive information, but there is no general alert that catches every name or personal detail you paste in. Checking what you share with Copilot is always your own responsibility.