The reaction between nitric acid and calcium carbonate results in the formation of two products: calcium nitrate and carbon dioxide gas. The chemical equation for this reaction is:

$$2HNO_3(aq) + CaCO_3(s) → Ca(NO_3)_2(aq) + H_2O(l) + CO_2(g)$$

Therefore, the name of the salt formed by nitric acid and calcium carbonate is calcium nitrate.