To get this matter resolved you are going to have to get yourself an attorney and get yourself turned in on the warrant. Then start assembling information including witnesses if possible as to where you were when this property was rented. If you were not in the area it ought to be fairly easy to establish that you were not the person who rented the property. An attorney can advise you as to other specific things that might be able to be done; one thing that comes immediately to mind is getting your handwriting compared with the signature of the other person on the rental agreements. Not addressing this situation is what is going to result in your ending up arrested on the warrant, and perhaps staying in jail until the case is resolved.
So sorry to hear about your situation...unfortunately, this has happened before to others...your first order of business is to contact a local attorney who can deal with the State Attorney's office and provide the necessary evidence to prove that you are not the person who committed the crime that the warrant was issued for. I worked in the Clearwater SAO office for 15 years and am extremely familiar with the steps you need to take to clear your name and finally put that chapter of your life behind you...please contact me at your first convernience at 727-822-3700.
Robert Heyman, Esq
Although it is quite rare, it is possible that the State will petition the Court to withdraw a warrant it has issued. There are various ways to attack your problem, but the biggest problem facing you is that this warrant is most likely "off the radar" of both the original detective on the case (who would have asked the judge for the warrant) and the assistant state attorney (who generally doesn't even know of the existence of a warrant until an arrest is mede on it. Also, it is possible that there is not an active case number at the court, so it may be difficult to determine the "facts" that were alleged in the affidavit supporting the Judge's decision to issue (sign) the warrant. For all these reasons, you probably will be best served by hiring an attorney to jump through the hoops for you.
Doing nothing, as you've already found, will only end up causing you trouble. Good luck.