Some first names find their inspiration in mythology Greek or Roman, one cannot consciously leave side the history which refers to such or such belief. Cassandra (Cassandre in mythology), was condemned by the Gods to be able to predict the future without never nobody being able to believe it. In France this first name was refused a long time because Cassandre could announce only misfortunes and the plagues. No one is need to recall it to what returns Abraham, certainly it is not very used in France but one finds it nevertheless anchored in certain families.
We find of the Narcisse, of the Diane, Orphée... To my knowledge no name of Gods: Zeus, Mercury, Apollo, these names are in general reserved for the animals, but the phantasm remains present. When parents are in the search of a first name and that a dictionary of mythology their tomb between the hands, they will very often go to the meeting of a hero little known, whose history reveals a hidden unconscious phantasm, a regression towards childhood. The first name of the son or the girl will be the unconscious projection of a "role" that the father or the mother played petit(e) and more often a current projection of oneself. One is identified "in his dreams the most hidden" with this character, the child while becoming the illustration, the concretization.
An example related to mythology has surprised me. It is about a woman originating in Haiti, she fell pregnant and did not worry about the choice of the first name of his/her child. With the birth, the small girl hardly weighed more than one kilo. She lived her childbirth like that of a baby miracle. And without reflecting A fore-mentioned Chloé Grace. But never knew why it makes this choice and which was the origin of this double first name. Chloé A returned just to a name of perfume (Narcisse).
Chloé is a first name appeared in the Thirties in France at the same time as Daphné (he also of mythological origin). It comes from young Greek the "plants". It would have been given to a mythological plant whose seed remained a long time under ground before germinating then pushed very quickly.
We find a double mythological association, Chloé with Narcisse, Chloé with the plant.
As for Grace, it renvoit at the end "with the grace of God", touched by the grace of God, expression which one uses in connection with the miracles or the miraculées people.
The chance of this first name Chloé Grace, is not any more one. But the real origin was unknown of the mom and did not know what wanted to say these first names nor from where they came. However the first name is appropriate to the event of the birth of this child and sound very weak weight.