As a general contractor license holder in Florida, you must normally be the one to obtain the permits. Homeowners can only obtain permits themselves if they are doing the work themselves or if they have family and friends who don't get paid for their work. Depending on the scope of your work, obtaining your own permission means that, in the eyes of the jurisdiction, you are the contractor for this project. Legally, you are now responsible for overseeing the entire construction project and are responsible for any injuries or poor quality workmanship you fail to comply with with the building code.
This means that if something goes wrong, you could face heavy fines and hospital bills. In most cases, the permit must always be obtained by the authorized contractor who is doing the work for you. The only exception is if you're doing a minor renewal yourself or with a couple of friends that you don't pay for. If you obtain the permit, you will be considered a contractor (at least in the eyes of the city) and you will be responsible if there are any construction problems. Contractors are also often familiar with the process and with city inspectors.
The contractor's pre-existing relationship with the city can be beneficial to you.