If you find yourself taking over a cluster with a name that is silly or doesn’t make sense, you can rename it without much issue. Your main thing to watch out for are backup software that target the cluster (such as Veeam or DPM). You just need to ensure they are reconfigured to use the new cluster name. Also, if you happen to have VMM managing the cluster, make sure you remove it from VMM before doing the rename and then add it back in.
To do this, simply open up the failover cluster manager, right click on the cluster and click properties. Now you can enter a new name. Once done it prompts you to restart each node in the cluster and you should do that sooner rather than later to prevent issues.
Hope that helps.