It doesn't seem like we need to make the connection count unique per push manager.  We could just name the connection like this:

this.name = String.format("ApnsConnection-%s-%d", listener.getName(), ApnsConnection.connectionCounter.getAndIncrement());

So in our logs we would see:

"ApnsConnection-Sandbox-1"
"ApnsConnection-Enterprise-2"
"ApnsConnection-Sandbox-3"

versus

"ApnsConnection-Sandbox-1"
"ApnsConnection-Enterprise-1"
"ApnsConnection-Sandbox-2"

Which seems like it will work great and doesn't involve the more complex static methods for keeping a mapping of push manager -> connection count.