There's very few things these days that ever require certified proof of marriage, so his concerns are unfounded, but if you did and you got someone very strict you would have to present your current ID, certified name change documents, and your marriage certificate. Otherwise the only issue you have is when dealing with some things people may assume you are not married or if you have kids they may think they are not yours. Things like traveling aboard with your (hypothetical) kids could be more difficult without additional paperwork. It's irritating, but certainly not the end of the world.
Otherwise I'm sure your husband is thinking of excuses since he is frustrated with the situation. It would be natural for him to think that if your ex's name was good enough why wouldn't his be. The name you chose is a personal decision, but if you are letting your previous divorce effect that it isn't always the best mindset to start out a new marriage.