I do not recall that information being available in any of our current libraries but feel free to make a feature suggestion here https://community.dataminer.services/feature-suggestions
In the meantime, an option could be to either use the option from Tom's answer or alternatively you can use the following snippet that uses SLNet
var request = new GetInfoMessage(InfoType.DmsConfiguration);
var response = engine.SendSLNetSingleResponseMessage(request) as GetDmsConfigurationResponseMessage;
string clusterName = response.ClusterName;
You can use engine.SendSLNetSingleResponseMessage if you are using an automation script or protocol.SLNet.SendSingleResponseMessage if you use a QAction or a corresponding method depending on your source.
Note that SLNet messages are internal calls and we do not recommend using them, as they are not officially supported and we cannot guarantee that they will still work in the future as these are subject to change without notice. We recommend to use instead always the correct UI or automation options provided in DataMiner Automation or through our web API when available.