She thanked men—good! but thanked Somehow—I know not how—as if she ranked My gift of a nine-hundred-years-old name With anybody’s gift. Who’d stoop to blame This sort of trifling?
Women (and girls) of nobility were meant to show appreciation and be impressed by the immediate men in their lives, such as family, their husbands, and on occasion, men who served them after great acts of duty, such as military feats in war.
The Duke is masking his anger and lack of control over the Duchess--he believes his "nine-hundred-years-old name" should warrant complete control over her, and is offended over the fact that she'd "thank men good," without any explanation over what she would thank them for (not to mention, she is fond of many "trivial" things, not just men, as he lists them before making said statement).
For historical context, the Duchess, Lucrezia is about 13-16 years old depending on when these offenses take place; she has yet to reach emotional, mental, and physical maturity. Without considering the Duchess's age and her lack of experience, he took her behavior as uncouth and as an affront to his dominance. The Duke's reaction lacks emotional maturity as he lets his jealousy be the vessel in how he treats his wife.