In a mobility group design, it is essential that all Wireless LAN Controllers (WLCs) share the same mobility domain name to ensure seamless client mobility and roaming between WLCs. This allows for clients to be recognized across the network and maintain their sessions as they roam. Additionally, when WLCs are in a Stateful Switch Over (SSO) high availability pair, they must use the same virtual IP address to present a single network entity to the wireless clients, ensuring uninterrupted service in the event of a failover.