Your identicon/Gravatar is based on the MD5 hash of your email address. As long as your email remains the same, your identicon shouldn't change (except when we get replaced with monsters and unicorns for fun). If you want a new randomly generated one, simply changing your email would be the easiest way to manage that.
Many email providers allow plus-addressing-aliasing
firstname.lastname@example.org. They'll still go through to you (if your provider supports it) but it'll look like a different address to the Identicon system.
And some email providers have out-of-spec addressing quirks. Gmail ignores
. characters in the username so you could be
u.s.e.r.n.a.m.e and Gmail treats it as the same thing.
Or you could just set an image manually of something you do like. An image of you, your pet unicorn, or some such.
Whatever you do, test the address before setting it. We'd hate to need to contact you and have our emails bounce. And don't do it too much. I know who I'm reading by subconsciously glancing at their gravatar. If you change your gravatar every other day, people won't be able to build that association.
As Robert points out in the comments, if you don't have an email address set, the system will use your IP address. That's generally not a great idea because you could see conflicts with other users, and it'll likely change over time (reducing the amount it actually identifies you).
I'd strongly recommend setting an email :)