No. Coronet is a big prestigious city, it makes sense lots of other places might name their cities after it. As can be seen with the city York.. Which actually isn't a very big city but is pretty in places and has a very nice Viking museum.
In the uk there is New York, Lincolnshire, New York, North Yorkshire and New York, Tyne and Wear.
In the USA there is New York City, New York, Texas, New York of the Pacific (renamed Pittsburg, California) and the amazing city West New York, New Jersey.
I suspect there are cities elsewhere named new York too. Anyway, as there is no canon information fir the name of alurion's capital, I picked it out of the hat.