This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
It looks like a leak, but one cannot be sure from the information you have given.
Does your application have a good reason to store more and more data or should it run in approximately constant heap space? If the latter, then leak looks likely.
Has a full GC been done? The drop in the middle of the graph looks like a GC, though it could be due to a real change in your application's behaviour - again I can't know without information about your application.
Betty Rubble? Well, I would go with Betty... but I'd be thinking of Wilma.