Yes, you are right.
When you dissolve a salt in water you don't change water's chemical formula.
You are simply making an aqueous solution of sodium and chloride ions.
Lets discuss this property in detail:
When you place a salt (i.e. sodium chloride) into water the sodium and chloride ions are surrounded by the partial charge of the polar water molecule causing the sodium cations and chlorine anions to be dissociated from the ionic solid and suspended as ions in the solution.
The salt may be separated into it's individual ions; however, this doesn't mean a chemical change has occured. When the water is evaporated, the sodium cations and chlorine anions will form the ionic solid
Here is a video which provides an animated look at this process.
video from: Noel P.