Is the united states of america so named because the union won over the conferederates in the civil war?

someone told me if the confederates won, we'll be called the confederate states of america..i argue not since the name united states of america is already stated in the constitution, w/c was ratified in 1787..the civil war ended in 1865..so no matter what, it'll still be the US of A..unless the confederates change the constitution..am i right?