The pure form of Buddhism involve no God or Gods. It's a contemplation of one's life and to meditate on one's life's path that hopefully helps you transcend above materialism of this earthly life full of suffering.
Buddhism and Atheism don't conflict. You can be an atheist and be very conscious about your life's choices in terms of becoming less materialistic and more thoughtful.
There are no rules of behavior that apply to all atheists because it is not an organized religion. Some atheists are very respectful of others and some are not.
仏陀(pronounced buddha) or 仏(hotoke)
An atheist does not believe in God.
Bouddha
Even atheists still say 'thank God' because the words are overly used in the society, but to atheists, the words are just words; they do not mean much.
The Buddha would be the right way to say it. "The Buddha" is a title used in the same way as other titles such as "The President" or "The Pope" when referring to the individual by title and not by name.
Often they say come variation of "Would you like Kleenex?" or "Allergies?" the Christian custom of pronouncing a blessing on the sneezer to ensure they haven't coughed out their soul is not a tradition with atheists.
Big Belly Laughing Buddha in Chinese language....
Most do. Except, most don't say the "under God" phrase.
In religious texts, God's perspective on atheists varies. Some believe that God may view atheists as individuals who have not yet found faith, while others believe that God may see atheists as individuals who have chosen not to believe in Him. Ultimately, interpretations of God's views on atheists may differ among different religious beliefs.
Buddha is considered an incarnation of God by the Hindu scriptures. Buddhism is for the benefit of the atheists. Buddhism is an atheist religion, but they follow Buddha's atheistic teachings.
Nothing, why should it concern them?