Of course, they have flight numbers, though the destination and the departure time was a good heuristic until it was not. I am much better at remembering the departure time than an arbitrary sequence of letters and numbers.

My home airport is a major hub; it is very common for some destinations to have a dozen or more flights across the various airlines. Quite often the American and United flights are scheduled similarly and leave within 30 minutes of each other.

I don't think this is that uncommon, so I've only ever paid attention to airline and flight number. I would recommend everyone else do the same.

Flight arrival and departure times can change suddenly without ample notice. That was never a good way to locate your flight.

The flight number is on the ticket/boarding pass.