Have you already checked the bottom of the mouse? The manufacturer and model number are usually printed on a label underneath, or sometimes inside the battery compartment.
If there is no label, connect the mouse by USB or its wireless receiver if possible, then right-click "Start" > "Device Manager" > expand "Mice and other pointing devices" > right-click the mouse > "Properties." Check the "Details" tab and select "Hardware Ids" or "Manufacturer" from the drop-down list.
If you are trying to pair it through Bluetooth and Windows is showing many device names, do not select one at random.
To help narrow this down:
- Is the mouse Bluetooth, or does it use a small USB receiver?
- Is there any name, logo, or model number printed underneath it?
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Thanks!