I know them as "roger beeps" from CB radio terminology.
Roger beep is a tone that is generated by the transmitting station when user lets go of the PTT (in similar way to Quindar outro tone). Using this tone to control anything in CB/HAM context is not really possible because there is essentially no standardization of how the beep sounds. Also IIRC having roger beep turned on is mostly frowned upon on ham bands.
Except the Roger beep coming from the repeater, which is semi-important in that it denotes that the repeater has unlatched and the transmit timer is reset.
If a repeater user keys up before hearing the Roger beep, the repeater doesn't restart the transmit timer, so there is a chance that your transmission will time out.
I've always thought that the beeps at the end of a user-initiated (not repeater) transmission would be cool, but they are indeed frowned upon. They aren't necessary, anyway. I'm sure if they became necessary for any reason, hams would be on the cutting edge.
Interestingly a digital mode called JS8Call uses framed transmissions, linked together, to send text over HF. At the end of a frame set, an ascii diamond is transmitted to signify EOL. Otherwise the receiving station doesn't know if they are done, or if they dropped a frame, or what. Not audible of course.