At present it is using "New Storyboard" and I would like to change this to be the name of the storyboard itself.
Thanks for sending this question in. I just wanted to let you know that I was able to confirm what you are experiencing, but unfortunately there currently is no way to get around this. The subject line of a distribution notification is always system generated.
I've gone ahead and created an enhancement request for this:
#207161 Customize Distribute Email Notification Subject Line
I know this probably isn't the news you were hoping for and I apologize for any inconvenience this lack of customization may cause.
Please let me know if you have any questions or concerns. Have a great day/weekend.