A MAC-Adress is never given by a Server to a Device.... It´s the IP-Adress, which must be uniqu in an Network, equal its local or global WWW.
A MAC Adress is also a unique Adress given to an Hardware, in best case hardcoded in the Hardware itself, and can´t normally be changed. And those MAC-Adresses had to be bought and given to the Hardware by the Manufacturer. Every network able device in the world has its unique MAC, so a device can be identified with it.
This makes the DHCP possible to block devices from an Network by MAC-Filter. Without Filter every device connected to the network is given an IP (by Server or provider, etc..) to enable communication between them. And those IPs had to be also unique in the Network.