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.