There are links to several prior questions with answers for somewhat related issues right below this answer - look at them too for more info.
Obviously you can call the bond on the contractor you were contracted with - the other one who actually signed the permit could thereby be considered to be either a co-contractor or an accessory to fraud and therefore also liable to you for damages, so I would say a good attorney could successfully go after both - both to call the bond, and against their liability insurance also due to the fraud. Plus to put additional pressure on them fraud charges could be filed criminally, as well as with the licensing board (usually state) and with the city business license and/or building department to get the contrator licenses suspended or revoked, and to have the city possibly ban them from applying for building permits in the city again or getting a business license.
There is also a remote possibility that, due to the fraud, if they were not bonded or insured or you don't get full recovery from their carriers, because fraud was involved, your homeowner's insurance might be a source of compensation of last resort for actuall damages, though of course not for the cost of actually getting the work completed.
One other thing - in some states there are contractor fraud compensation funds to help people in your situation - be sure your attorney checks on that, or google it yourself - usually at the state contractor licensing board level.
