"If I’m using a persistent subscription, what is the purpose of the group name?"
You can have n subscription groups / stream (each operate
independently and can have different configs etc). As example
consumers a,b,c connect to stream foo group dc1 consumers d,e,f
connect to stream foo group dc2. The subscriptions are totally
separate from each other.
Also, If I disconnect the client from the server will it try
reconnecting if it is reconnected?
The client or the subscription? The client will reconnect but the
subscription needs to be reconnected.
Finally, are there any bench marks as to how many messages per second
ES can handle?
This depends heavily on your hardware setup. Local disks are faster
than remote and usually disk is the bottleneck. It also depends
whether you are batching messages etc. Using single event per message
I can get about 50-60k/sec on my desktop pretty easily.