This is a common fish in the Caribbean. I have seen it many times while SCUBA diving and snorkeling.
Scientific name:
Acanthurus coeruleus
Professional image:
https://reefguide.org/pix/bluetang14.jpg

My images:
On approximately March 4, 2014 at: I took the following image:

On approximately March 4, 2014 at: I took the following image:

On approximately July 3, 2017 at: I took the following image:

I am pretty certain that this is a Blue Tang. There is a chance that it is an Ocean Surgeonfish.