Betty. 
Fob
Fob
A dooter, and the act of using it dooting.
Boops are for noses.
Clicker
I call it a remote. The people who call this ‘the beep-beep’, are they adults?
That is one of the funniest things I’ve read today, but then I am easily amused.
IMHO, you’re thinking of the term watch fob.
In answer to the OP’s question, I call mine an ‘alarm remote’.
Key fob. I actually have to use a key to unlock the door. I also have hand crank windows. My mirrors require hands on adjustment too.
No rumble seat and crank handle? ;)
I call it the “(key) fob.”
Hey, Antigen said she calls it “the beepy thing” 
Most of the people I know who call it “the beep-beep” are retirement-age adults. They will also use the expression to refer to the whole mechanism, as in “his car has a beep-beep but the van is older, it doesn’t”. Or, when they lose something and referring to the practice of using the remote to echolocate your car in a public parking lot, “I need a beep-beep for my glasses!”
Car Key.
I call mine “Diedre”.
So how many of you still call the TV remote a ‘clicker’?
I used to just call it the remote but my wife calls it the clicker and it’s rubbed off on me a bit.
Well, exactly. (OP here.) I actually meant, originally, what does “one” call it, and now I know, so thanks to all. I should have thought that people would have their own names (eg, the clicker for the tv).
So, if I’ve read correctly, some people here might say, “Hon, the fob isn’t working.” But that’s just a guess–it probably doesn’t come up in speech that often: “Hon, where’s the fob?”–I doubt it, but what do I know.
…(crickets)
Unfortunately, your mic is on. 
Scientist banned from revealing codes used to start luxury cars
High court imposes injunction on Flavio Garcia, who has cracked security system of cars including Porsches and Bentleys
Lisa O’Carroll
guardian.co.uk, Friday 26 July 2013 13.18 EDT