Bothered: My husband wants me to include his name in my documents as well as my ID

I recently got married after two years of dating but there is one thing that is bothering me. My husband wants me to include his name in my documents as well as my ID. From the few people I have sought advice from, I have been discouraged from doing it as our marriage is still so young. My husband has demonstrated his commitment to this marriage by including me in his documents as well as allocating me shares in his company. I know I sound like a pessimist but I need guidance on the best to make at this point.