When you say that someone is a 'Fuddy-Duddy' you mean they are a stuffy of foolish-acting old-fashioned person.
Example of use: “Get with the times! You don’t have to act like an old fuddy-duddy.”
The expression 'Fuddy-duddy' is of American origin, with the first printed instance being found in an 1889 copy of Texas paper The Galveston Daily News: “Look here; I’m Smith – Hamilton Smith. I’m a minister and I try to do about right … I object to being represented as an old fuddy-duddy.”