Your maiden name on your ID will not cause any issues with processing your tax return as long as you used the right information from your social security card as your tax return. The IRS matches tax return information with the Social Security Administration. Your Federal return does not actually require a driver's license in order to process your return. They are asking for the license information because its an added safeguard to help fight identity theft and could help speed up processing of your return when you supply the information. But, if you are worried, then you can just skip the license entry page completely by leaving it blank and hitting continue.
