When converting greetings and leave-taking into indirect speech, we use such verbs as to greet, to welcome, etc.

Direct Speech Indirect Speech
She said to them, “How do you do?” She greeted them.
He said to them, “Happy to see you at my place.” He welcomed them.
He said to them, “Goodbye!” He bade them goodbye.
He said to them, “Good night!” He wished them good night.