You have to be precise about these things. Carmen isn't Hebrew, it's the SPANISH version of the Hebrew Carmel meaning 'garden' or 'orchard' in Hebrew. Carmel is the name of a mountain in the Holy Land near Haifa which was populated from early Christian times by hermits who later organized into the Carmelite order of monks. Carmen was altered by folk etymology to the form of the Latin word carmen meaning 'song'. It is sometimes given as a name from association with Bizet's tragic opera heroine but it wasn't his 'fancy' - the opera was based on a short story by Prosper Mérimée.
If you find flaws in the site you're welcome to report them but be prepared to back them up with far more than just 'I know the meaning of this'. Research is based on resources beyond oneself. For a classicist music lover who bestows the name Carmen with the Latin meaning in mind then it indeed means 'song' in that instance. Look up any dictionary entry and you'll likely find at least 2 meanings, both of which apply in different contexts. Names are just words, refined.