With normal (non-bluetooth) wireless mice & keyboards, each mouse and receiver pair is supposed to be uniquely coded, so if several people are using the same type in the same area, they do not affect each other.
(Imagine a business office with dozens of computers, if the mice were not each paired to one specific receiver! )
Some older types have "pairing" buttons on both the receivers and mice or keyboards, so any of that series can be linked together.
Newer ones are usually uniquely coded and paired at the factory - or are supposed to be unique, anyway.
The only present types which are user-pairable are bluetooth ones.
The pairing or disconnection is then done through the bluetooth software on the computer & the mouse only works with the machine it is paired to.
For anything that already has built-in bluetooth, like many laptops and all-in-one PCs, you do not need any extra USB device (even if it's supplied with the mouse) - you just pair it to the computer using the Bluetooth tool in the control panel.
If by chance yours are bluetooth, then you should have a bluetooth icon in control panel that shows the mouse connected.