You're suggesting an entire country of millions of people change their phone numbers because America decides that it wants to create a new international area code which happens to match the word "moon" in English?
6666 is meaningless for people who speak French (that would be lune, 5863), or German (Mond, 6663), or Spanish (Luna, 5862). The rest of the world would be quite happy with say +83 for interplanetary codes.
Perhaps America should change its country code from +1 to say +889, and open up +100 through +199 for others.
Isn't the + a shorthand for the international part of the code, which changes per country. My country (oz) it's 0011 (and faxes were/are 0015).
So you don't need to create new country codes or boot countries into new prefixes, but just supply a new interplanetary prefix.
Who decides what parts of the moon get what area codes?
Imagine how long it will take to get Orange to instal a landline in a crater!