Hi dnicholson!
First of all - I'd like to thank you for reaching us and showing your expectations as to the behaviour of the application 
For some time already we have been reviewing, rethinking and (re)working on Jira Software, focusing on transparency of user actions, user supervision && data visibility. While scanning trough all the feedback we received related to those areas I have found your request and believe I have two, hopefully good, pieces of information that could be of a hand for you.
1) if you're interested in getting to know "who closed the sprint" - this information is available in the system for a while already. We realise it might be not that obvious to find it - therefore we created a dedicated KB article that explains in details all the ways one can obtain such information.
The knowledge base article can be found here: https://confluence.atlassian.com/jirakb/checking-who-closed-a-sprint-947165301.html
2) if you are interested in getting to know who started or reopened the sprint - this information is not directly displayed anywhere in the system… yet.
But we realise it is crucial for the team members to be aware of what's going on with the sprint, who (and when) starts or re-opens one and therefore - we will include this information in a similar matter as in point 1).
The updates are already developed and are currently undergoing extensive tests. Moreover - we want to make the available as soon as possible - hopefully with next Jira Server release.
Once that's done - we'll also update the KB mentioned above so that you can find all the relevant guidance in one, simple article.
I hope this solution will help you to better understand what goes on within your team!
Best regards,
Michal
Sr. dev @ Jira Server TEAM
Hi all!
Thank you very much for your feedback and votes of support expressed in this request.
I'm glad to inform you that as of 7.10.0 Jira Server release all previously mentioned improvements are "live" and available for use.
I honestly hope this will satisfy your needs.
Best regards,
Michal
Sr. dev @ Jira Server TEAM