Each person can create their own list any way it makes them happy but using only common names can be very confusing; the names may be regional and not recognized by folks in other parts of the country (or the world). It's always best to include the botanical name, or at least the genus if that's all that is known, whether first or second so folks know what they are getting in the swap.
Using the names that are in our database will help others to find the data needed such as zone hardiness, height, plus photos, etc. and may result in a better swap result.