I recommend EZ-OFF oven cleaner in the YELLOW can (not the blue can since it won't take off the paint). Mask the area immediately below the lettering and tape on some additional paper towels to absorb the runs. Spray the area with the oven cleaner, wait about two minutes and remove with a METAL scraper blade (a plastic one may dissolve). Remove the masking and clean up any residue with acetone. Follow up with a wash down of a 1/4 cup of baking soda in a gallon of water and rinse thoroughly with plenty of water.
Unfortunately, regardless of the method of removal, you'll likely see a shadow of the old name. Use a good frp cleaner such as 3-M's Finessit and the shadow will be diminished with brighter gel coat surrounding it. The remaining shadow will fade out over time, the length of which depends on how long the old name was on the boat. DON'T REWAX THE BOAT UNTIL AFTER YOU HAVE APPLIED THE NEW NAME!! Both paint and vinyl need to adhere to clean gel-coat - not wax.
When you apply a new name in vinyl, use only high quality CAST vinyl lettering and not the cheaper calendared vinyl lettering that some of the discount sign shops sell. Even in Florida's sun, good vinyl boat lettering should last about 7 years without fading. Hope this helps! GOOD LUCK!!