Form 2553 must be filed no more than 2 months and 15 days after the beginning of the tax year that you would like for it to take effect or anytime in the tax year before the year you want it to take effect. For example, if you want S-Corp status to take effect for 2018, you must file the form no later than March 15, 2018.
Prior to filing form 2553, I would definitely file a correction of the business name for the EIN. If the name does not match, the IRS could kick back Form 2553 to you. From the IRS website, it looks like Form 8832-B should be filed to make this correction but I would just give them a call to double check.
All the Best-