Funny thing, there is an article made by an american living in Sweden that wondered about Rhode Island-dressing and the name, he even wrote the company about it and their response was (sic)

"Thank you for your e-mail and how nice to hear that you seem to appreciate our products!

Classic Rhode Island sauce has actually nothing to do with the state of Rhode Island in the US. It is a Swedish innovation by our well-known Swedish chef Tore Wretman. Wretman was also one of the founders of the Academy of Gastronomy. Tore came up with the basic recipe of Rhode Island Dressing which since then has been developed in many ways.

I hope you enjoy living in Sweden 🙂

Have a wonderful day!

Best regards,

Orkla Foods Sweden"

Not even the company that makes it has any idea why it's called "Rhode Island".

We also have Bostongurka (Boston cucumber), a cucumber relish made by the same company that was created in the manner you describe, the creator just wanted to make something "american". There's also "Budapestkaka" (Budapest cake). It has no origin or equivalent in the city of Budapest, the baker that created the cake just happend to love the city Budapest.

The company that makes Rhode ISland also makes their own Thousand Island dressing, but that one contains cucumber. Rhode Island dressing does not.