Aug 20, 2018 - 11:48 AM
It's a good thing that you recognize the need to customize your cover letter to the company. Although you've made a mistake, your response to the mistake could positively impress the hiring manager. As soon as you realize you've slipped up, reach out to your contact, admit your mistake, and correct it. This means sending the correct cover letter and, perhaps, sending a written explanation.
Remember that one of the best ways to handle a mistake is to avoid making one in the first place. Do this by carefully reading through your document and having a peer read through it as well. You may also take advantages of resources such as this one from the Purdue writing lab and this guide from LiveCareer.
Jan 29, 2019 - 11:25 AM
Let’s go further on this topic. If you applied online via an online application system, log in to the online system. Look to see if you have the ability to update your cover letter there. If you don’t, you may want to consider submitting a second application with the correct cover letter. This would mean resubmitting not only your cover letter but your resume, too.
If you submitted your cover letter and resume to a friend at the company, one who is acting as a referral for you, ask your friend if he/she has already forwarded on your cover letter and resume to the hiring manager. If they haven’t yet, send your friend the new, revised cover letter.
If you emailed your resume and cover letter directly to a recruiter or hiring manager, resend the correct version of your cover letter. In the body of the email, explain that there’s an error in the cover letter, and apologize for your mistake. If there’s a chance they may overlook the mistake, you may want to email them with an updated cover letter, but not point out the specific error. This would allow you to submit your cover letter, while drawing the minimum amount of attention to the error.