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No favorite names yet.
Have a safe delivery.
I like the suggestion of using another W name to go with Wyatt. I personally would avoid another A first name as the Wyatt would be left out.
Other names you might like... Xavier, Marcus, Logan, Dallas, Maximus, Owen, Emerson, Liam, Ivan, Ronan, Luke, Lincoln, Dante, Hector, Elliott, Darius, Levi, Elias, Felix, Samuel, Tristan, Evan.
I myself really like Wyatt James out of the two names.
Congrats on your twin daughters.
I absolutely love the name Luna. I have it on my own list. Ivy is also on my list. Celeste is a name I like as well.
I am not a fan of Skye myself, but if you love it, use it. It is important to name your children names which you love. Lynn is nice though. One name that comes to mind you may like is Skylar/Skyler. As for Claire I do really like the name but not paired with Skye Lynn.
The only thing I would change about your names is to change Celeste and Claire around so it would be Luna Ivy Claire and Skye Lynn Celeste.
Good luck with your twins and hope you have safe and easy birth.