Although you could technically use a pseudonym, (as long as it's not for the purpose of defrauding anyone), it could present many obstacles for you when trying to enforce contracts and could create confusion with financial institutions. Further, you may want to check with the Secretary of State to determine whether the fictitious name has been already registered.
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I would recommend that you conduct business using a Doing-Business-As ("DBA") or Fictitious Name designation that is registered with the Florida Department of State: Division of Corporations . The problem isn't necessarily only that you're using a name different from your own (which is a logistical problem for obtaining bank accounts and things of that nature), but also that you could theoretically expose yourself to claims of fraud and the like in a lawsuit. It's not hard to imagine an instance where someone claims (rightly or wrongly) that you failed to deliver a product/service that they paid you for, under a different name, and the attorney on the other side locks onto a fraud claim and you spend the better part of a year in litigation fighting something that could be prevented right here. I usually recommend a "better safe than sorry" approach when setting up a framework inside which your business will function – it saves money, headaches and time in the long run.
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As my colleagues have pointed out, a pseudonym used in certain industries may give the inference of fraud or deceit. However, Florida has a mechanism in place for setting up businesses using a fictitious name. You may register one that isn't taken and conduct business under that name.