I found out recently that in my state, the online vanity plate checker shows plates that were PREVIOUSLY registered but NOW available as NOT available. I wanted to get one of my own plates I had years ago and assumed there was some process to have it transferred, but was told by a DMV rep that after two years of non-registration, they're up for grabs. Apparently the web page does not take this into account.
That means there are probably a lot of great plate names up for the taking that people are just assuming are taken. You'd need to call the DMV to verify.
Hopefully Florida's web page does not have that limitation.