This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma 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.