Welcome!
First of all, I think it's important to talk to your wife, but beyond that, it's surely not necessary to share the information with anyone else. I am no longer ashamed that I am an alcoholic, but, it is just a part of who I am and I choose to focus on other things. Other than my husband and two adult children, I have told no one in my life about my addiction. That wasn't my decision early on, but as time went by I realized what a personal journey recovery would be.
If alcohol is causing problems in your life, then stopping drinking is the best answer.