How can you participate in this wonderful "Let's get the general public interested in radio astronomy" opportunity? Well if you follow this link you can find where to go to submit your own name, and perhaps they may just consider it. I know that I will be submitting one or two possible names. They have to be in by December 1st, and they will announce the result at the AAS (American Astronomical Society) meeting in January.
As a side note: In reading a news story on the BBC about this announcement I found this paragraph quite funny,
"The astronomy community has a long history of descriptive yet fairly unimaginative names - including the VLA itself, the Very Large Telescope in Chile, and the yet-to-be-built European Extremely Large Telescope (the design for which was chosen over the alternative Overwhelmingly Large Telescope)."