if I sell to open a contract and the buyer buys to close a contract, will I get notification?

if I sell to open a contract and the buyer buys [sic] to close a contract, will I get notification?

This doesn't make sense. The buyer doesn't BTC the contract. (Only you and other sellers can BTC the option). They can exercise it early, though. They call their broker and let them know that they want to exercise. Normally they won't do this, because they gain more from selling the contract than exercising it; the contract has time value (extrinsic). They'd be forfeiting this value, so they must have a good reason and strong desire to own stock in the case of an early exercise on a call.

You may have meant the following:

if I sell to open a contract and the buyer b̶u̶y̶s̶ [sic] sells to close a contract, will I get notification?

In that case, the problem in your understanding is that you don't sell a contract to an individual. When you sell a contract, you are opening a short position, but no one in particular is the holder of that contract. In the event that a holder of a contract sells and closes out their position (STC), it has no impact on you. It just means that they've transferred the right to exercise the option to someone else. Your contract is still open.

Another question could be:

if I sell to open a contract and the buyer b̶u̶y̶s̶ [sic] s̶e̶l̶l̶s̶ t̶o̶ ̶c̶l̶o̶s̶e̶ ̶a̶ ̶c̶o̶n̶t̶r̶a̶c̶t̶ exercises their contract early, will I get notification?

If they exercise the option early, you may be affected. Once again, you don't sell a contract directly to someone (although someone does typically purchase a contract at the same time that you sell one). If someone exercises early, their broker will give notice to the OCC, which then randomly assigns a market participant short of the identical option series (the same ticker, expiration date, and strike price). You may or may not be the one who's assigned by the OCC. If you're assigned, your broker will notify you, and your shares will be automagically sold to the person, early exerciser. This will rarely happen. Early exercise is not a particularly common practice.