You may also want to check your third-party mouse maker's website for Mac drivers. If you like having a different button as your right-click, you can customize which button is primary - left or right - in the Mouse system preference pane.
If you have a third-party mouse that has a right physical button, macOS should recognize the button and map it accordingly after you plug in the mouse. VPN Deals: Lifetime license for $16, monthly plans at $1 & more