Yes, you file a final return and mark it as final. Use the form your company normally files: Form 1120, Form 1120-S, Form 1065, or Schedule C with Form 1040 for a single-member LLC. If you skip it, the IRS can keep treating your company as active, which can lead to penalties, notices and extra returns in later years. Final payroll and 1099 filings are closed out at the same time, and after that you can ask the IRS in writing to close your EIN.
Inkle handles the state and IRS filings that close a US company properly.