‘ And Naomi took the child, and laid it in her bosom, and became nurse to it. And the women her neighbours gave it a name, saying, “There is a son born to Naomi,” and they called his name Obed. He is the father of Jesse, the father of David.'
And Naomi already had cause for blessing, for she acted as his nurse, coddling him and watching over him. And her women neighbours supplied a name for him because he was ‘a son born to Naomi', not literally, but because he was her grandson. The name means ‘servant' and the idea in the neighbours' minds would be that he would be like a true servant to his grandmother. But the writer probably also saw it as signifying that he was the servant of God, an that he proved to be a true servant of God, for he begat Jesse, who begat the great King David. He could in terms of those days perform no greater service.
Note that in Ruth 1:11-13 Naomi had made clear that it as unlikely for her to have a son. But now we learn from these verses that she did have ‘a son'. Even though he was not from her womb, she nursed him in her womb. God had heard the cry of her heart.