From someone who did birth certificates for 5 years in CA:
It can differ from state to state, but very little. But in order to cause fewer legal problems down the road, you MUST name the biological father on the birth certificate. You don't mention if the separation from your ex is legal (filed with the court) or not, and if FL automatically assumes that whomever you are legally and currently married to at the time of birth is the legal father, then your ex will be considered the father in the eyes of the state. And if that is the case, not only do you have to list the biological father, but you will need to do the DNA testing to prove it and the father will have to file a paternity petition with the courts. Or you can choose not to do any of that............just be severely forewarned that it could cause you serious legal ramifications down the road.
You can give the baby any last name you want, you can even hyphenate it with your maiden name and the bio-dad's last name....I've seen ones that didn't remotely resemble Mom's OR Dad's, but think long and hard before you do. This is something the child has to live with for the rest of their lives, so this is not something you can be selfish about.....you have the child AND the bio-dad to think about here, as well.
The birth certificate is a legal document filed with the state.......do the right thing by all the parties involved: the child, the bio-dad, and your ex. Technically, it really doesn't make any difference how the state looks at it (as stated in my first paragraph).....if you name the bio-dad on the BC, do the DNA testing, and bio-dad files the paternity petition, you will have sufficiently dotted your i's and crossed your t's legally.