If I short an option and the buyer exercises the contract, what will happen?

Let's say that I'm on TDAmeritrade. I short a call option to collect a premium. I also own 100 shares of the same stock in the same account.

So that's a covered call. Good way to generate premium cash flows.

In a week, the option is in-the-money and the buyer exercises it. What will happen in my account?

Normally they won't early exercise it, because they would forsake any remaining extrinsic time value. Usually they'll either sell it to another buyer (thus closing their position), or they'll wait for the option to expire hopefully deeper in ITM in their ideal scenario.

Even though early ex is a rare practice, it does happen sometimes.

A general nitpick: no particular person owns the contract you sold; the OCC randomly selects and assigns a seller in the event of an early exercise. It could be you; it could be someone else.

Will I get an alert from my TDAmertrade?

You will get an alert that you've been assigned and they've sold your shares at K_c on your behalf. Your holdings will reflect this.

Must I buy-to-close the option?

No, at this point after you've been assigned, you can unfortunately no longer have the ability to BTC the option.

Will the 100 shares of stock transfer to the buyer?

Yes, your broker does this for you automatically.