Wouldn’t it be better to request “an attorney of my choice” rather than “my attorney” if there is none specific in direct mind? Otherwise you are asking for a nonentity. And chiding for not having one in mind is not an answer to the question.
The statement that you want to talk to an attorney is sufficient for Miranda. It conveys the information that you don’t want to answer any questions without legal guidance. It doesn’t matter at that time if the attorney is the public defender or Zimmerman’s attorneys.