Hams definitely use 'over.' They're usually less terse about it though and will say "over to you." It makes it clear you're done speaking and waiting for a reply. Otherwise, if you pause for a moment, somebody might try to reply while you collect you thoughts and continue speaking (not hearing them, and them not hearing you). Sometimes, especially on repeater systems, it is necessary to take short breaks and rekey your radio because the repeater will drop out after about a minute and a half as a precaution against getting stuck on, so you might stop transmitting momentarily, but not be finished with your message and not ready to "hand it over" just yet.

The roger beeps at the end of these transmissions are redundant though (and very uncommon on ham radio, though sometimes you might hear a similar tone added by the repeater system to signal the end of a transmission). They are more common on commercial radio, public service, and FRS/GMRS. CB radios might have these as well, but there isn't much CB activity in my neighborhood. That said, I don't think I have EVER heard a roger beep on any frequency below VHF.

The callsign thing is true though. Hams are supposed to identify with their FCC assigned callsign every 10 minutes, and since these are listed in a public database this makes using funny aliases for anonymity impractical. This is definitely a CB trope, which has been aped by anybody who has ever bought a pair of GMRS radios at their local Walmart.

As for @BanSwitch2Buyers@hexbear.net's OP, in my headcanon these are guys involved with rural street racing (they're speaking in code, but not very robustly). They're talking about a couple different roads in the area which work well for this, probably the type of winding country roads with little traffic or cross roads, and virtually zero police patrols. The blue shell Lemmy is talking about is a NOS tank (canonically blue), or some other new untested performance upgrade to their car.