Engraving on the two wedding bands my Fiancé got me

My lovely Fiancé got me two wedding bands before our ceremony, one that is diamond that matches my engagement ring and the other is a gold band to match with his band. We are deciding on the engravings to put on the rings. We had settled on putting our name and a phrase on the gold bands but still going back and forth on the diamond band. He feels like I should put his name on that one too since he feels it's an even more preciouse ring than the gold band. I feel like it's redundant to have his name on my finger twice especially that the gold band is the one I am going to be wearing always. He is starting to get a bit hurt that even though he says that it's going to mean alot to him that I am not convinced. Is that usually what is done? Or is it really like I'm thinking, it's too much and feels extreme?