I assume that settlements that are of the form “[City]-On-[Stream name]” don’t count, because there are dozens if not hundreds of them in England, and at least some in Germany as well.
No, because “on” and “upon” and such are prepositions, not conjunctions. But if you can dig up any examples of [City]-and-[Nearby Thing of Importance] it would count.
Lots of bands. Flash and the Pan, Southside Johnny and the Asbury Dukes, Chad and Jeremy, Peter and Gordon, George Thorogood and the Destroyers, Tom Petty and the Heartbreakers, et al.
English Foods: bangers and mash, bubble and squeak
hot and sour soup
sweet and sour pork
nut’s and honey cereal
kibbles and bits
Truth or dare
Sonny and Cher
Donnie and Marie
Kith and kin
Huey Lewis and the news
Is macaroni and cheese (or spaghetti and meatballs) a singular thing? It’s certainly a dish, but macaroni is a thing by itself as is cheese. Similarly in your example, Trinidad and Tobago are each an island which have been merged into one country. Does every married (or perhaps not) couple I know count. Barack and Michelle; one thing? If so how about, Bob and Carol and Ted and Alice; does that count extra?
If you don’t know, Truth or Cionsequences used to be called Hot Springs, but changed its name in 1950 to that of a popular radio show in response to a dare/offer:
When I was a kid, Truth or Consequences was still on, having graduated to television. I thought the name of the town was strange and unconnected, until I read about it.