According to the MPC:
This discoverer is accorded the privilege of suggesting a name for his/her discovery. The discoverer has the privilege for a period of ten years following the numbering of the object.
As of 2006 June 1, all asteroids with numbers below (7041) that have not been named are eligible to be named by any member of the public. The list is here:
And for the names:
http://www.cfa.harvard.edu/iau/info/HowNamed.html contains a list of rules.
http://www.ss.astro.umd.edu/IAU/csbn/ and http://www.ss.astro.umd.edu/IAU/csbn/mpnames.shtml contain more rules and a contact email for the CSBN - remember, an individual/group should not submit more than two names per two months.
http://en.wikipedia.org/wiki/Main_Page is always a good starting point for a name hunt. Try to find something connected to the discovery circumstances or the object's orbit. Remember to write a good (yet short) citation.