What's the technical terminology for call-and-respond type behaviour? The groups of some species such as water birds display a behavior that once out of line-of-sight a member will periodically initiate an interaction by make some type of sound, which will be followed up by responses from all the other members - presumably to confirm they haven't been silently snatched by a predator. I have observed this in person at a local botanical garden where the water birds sound off like this every 10 minutes or so all day long. What is the technical term for this behavior and some examples of species that demonstrate it?

if you are referring to call and response in rapid succession, ethologist use the terminology "turn-taking" or "antiphonal calling". Many species do it with different degrees of precision. A rapid research on google scholar will give you several results. I do not know whether it would apply specifically to your case, which might be more general and it could be simply "contact calling".

Regarding the hypothesis you formulated ("(...)presumably to confirm they haven't been silently snatched by a predator"), it would be nice to know if actually everyone respond, who is calling first (always the same individual?) and if they would behave different if someone does not reply.

Hope it helps and have fun with your observations.