Ditto to everything that has been stated already!

You need to not only have fraud alerts placed with all three credit reporting agencies and Chex Systems, but also get copies of your reports.

https://www.annualcreditreport.com/index.action

If they are renting vehicles under your name it stands to reason they also have credit cards that match name on drivers license. Thus you most certainly have major ID theft going on... Oh and you need to contact your local state DMV to let them know what is going on and perhaps check your license record.

Oh and you need to contact local LE and file a report of identity theft, or see what they advise.