Is it correct to Everybody
How do you want to use it?

As a simple greeting, then
Good Morning, Everybody
is fine.

I said "good morning" to everyone.
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It is a good way to say good morning but it is very informal. You should just watch where you use this construction because it isn't wrong.

the sentence 'good morning to everybody' cannot be ruled out, but a better way to say this greeting is to say it without using a verb 'to'. you can say

good morning, everybody or simply good morning, they will understand