Ubuntu 13.04 probably won't arrive in full until next spring.
A tentative launch date for Ubuntu 13.04 has already appeared on the "R" schedule, just weeks before Ubuntu 12.01 "Quantal Quetzal" becomes a proper release on October 18. Naturally dates are subject to change, and so far Ubuntu 13.04 has yet to be named.
According to the schedule, Ubuntu 13.04 won't be fully released until next spring. The process starts with Alpha 1 which is scheduled to launch on December 6, followed by Alpha 2 on February 7. Then on March 7, Ubuntu 13.04 will supposedly arrive as beta, and then go into Release Candidate mode on April 18.
Finally, Ubuntu 13.04 is expected to officially release on April 25, 2013 – this will be a Thursday, which is Ubuntu's traditional release slot. Again, keep in mind that development on Ubuntu 13.04 hasn't even begun, and that this schedule is just a draft. Dates could change depending on how development progresses.
Mark Shuttleworth, father of the Ubuntu operating system, will be the one to announce the codename for Ubuntu 13.04. What that will be is anyone's guess at this point, but the schedule indicates that there's plenty of time to conjure up potential names before the first alpha arrives in mere months.