Hooray! They look beautiful I can't wait to see how the color on those favites develops - they're very pretty. Those duncans will be great as well, they grow quickly if well fed
Congrats on the new corals and the happy couple. BTW, your moon coral sure looks acanthastrea (acan) echinata. They are very aggressive corals so be careful with its neighbors. The first couple pics in this thread will give you an idea of what I mean ....
Pic is kind of far to see for sure but I am betting that is what you have. If you can get a closer pic (especially of the polyps) I will be able to ID it better.
There are several species of acans. Lords, bowerbanki, hillaes, rotundoflora and echinatas. You should be able to compare google pics to your coral and get an ID. Moon corals are favia type brain corals with distinct/rigid polyps...