The Alshich Hakadosh asks why Klal Yisroel is called the children of Avrohom Avinu, and not the children of Noach, whereas the nations of the world are called “bnei Noach”.
He answers that there was a big difference between Noach and Avrohom. It says that Noach walked with Hashem, meaning that he made sure to follow His ways. However, he didn't concern himself with the rest of the people of his generation. When he was told to build a teiva that would be 120 amos wide, he didn't daven to annul the decree because he was happy that there would be sufficient room in the ark for himself and his family. He wasn't concerned about what would happen to everyone else.
The pasuk (Yeshaya 54:9) refers to the flood as "mei Noach" (the waters of Noach). Chazal (Zohar Hakadosh 67B) explain that it was called by his name because he caused it. He could have cancelled the decree with tefillah, but he didn't attempt to do that because he was only worried about himself and his own family.
Accordingly, the nations of the world are called "bnei Noach" because they inherited this middah of only worrying about themselves, and not about others.
Avrohom Avinu, on the other hand, was concerned about everyone. In addition to his own avodah, he tried to help others. He even davened to save Sodom and Amorah. Klal Yisroel is called by his name because we aim to emulate him by worrying about others.
In this vein, Chazal (Zohar Chadash, Parshas Noach, 38B) say that when Noach emerged from the teiva and saw that the earth had been destroyed, he cried and said, "Ribono Shel Olam, You should have had mercy on Your creations."
Hashem replied, "You foolish shepherd. For 120 years, you were building the ark, and you never prayed for the people of your generation once. And now you are crying?"