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.