EAP TLS flow

I have a doubt regarding eaptls..
If I am doing tls authention. I would install server cert in the server (eg signed by GoDaddy)
If my client machine has it too, it will be authenticated.
Let's say there are two companies in a building both using same GoDaddy as server cert as well as client cert.. Would it make user one company a to connect to the ssid of company b since tls process both client and server have the valid cert... Does cn play any role here? If yes then where in the ad we mention that..