“Cold soups” is a weird term. They should almost never be served cold, they are served chilled so remember to take it from the refrigerator about 20 minutes on a hot day before you want to serve it.
Garnishes for this soup can and should be rather simple, chopped chives or thinly sliced scallion. Maybe a spoonful of finely chopped egg and parsley. But being American why not crispy chopped bacon or small cubes of ham in the warm version.
This is a long lost soup and a bit dated I have to admit. But it has most of the things one really wants from a summer recipe. It is easy, simple and inexpensive. Has very few ingredients to worry about and takes in totality about 20 minutes to make, 10 in the beginning and 10 in the end. The rest is just waiting to enjoy it.
This is also not Vichyssoise which is an American invention, a bastardization of French Leek & Potato soup which is made with water instead of chicken stock. It was after all a peasant dish with very modest origins originally. To make Vichyssoise use only the white part of the leek and replace the water for good chicken stock which produces a slightly deeper flavor.