Have a girl name picked out, but not sure what to tell people... please help?

My husband and I found out that we are having a girl and were really excited because we will be naming her in honor of his mom (deceased) and my grandma. Her name will be Cathryn Jane. HOWEVER, we plan on calling her CJ because we think that is cuter. I am finding it more and more difficult to tell people what we have decided because when I say "we're naming her Cathryn Jane..." they immediately say 'oh, that's so cute' and then I proceed to tell tehm that "we will be calling her CJ" but it's like they don't even hear it. Now I am hearing people say that we are naming our baby Cathy or Cat or Cate, ect. I am getting a little frusterated correcting people on her name before she is even born. We are not interested in changing her name or calling her any thing other than CJ. So should I just start telling people we are naming her CJ and not even mention the Cathryn Jane part... unless they ask what CJ stands for? What would you do?