I agree with Larry. AlexFans.com could have real liquidity; I'd run the name Alex through a kw tool, see who the volume searches are and x out the non-monetisable (Alex Jones occupies a number of the top spots in various phrases; safe to delete) then market the domain to fans where you can find them. One of the few domains I'd suggest putting on eBay, since fans of Alex Rodriguez et al. will be searching for the celebs' names when looking for memorabilia, collectibles, media etc. and it is precisely the kind of people who shell out money for a shirt or poster or Bobblehead with some guy who happens to be famous on it, who might also shell out money on a good domain on which to build a fan site.
Because of the highly generic nature of the name, as long as you yourself market it as "for fans of any sort of Alex" and simply optimise the marketing for the specific celebrities, I wouldn't think you'd run across any kind of issues with mark holders.
Frank