What are my legal rights when a business owner replies to my review and post my name in the reply.

I placed an order on an online business and had a bad experence with the a representative of the company. I posted my review and explained my experence with the rudeness of the represenative, I didn't write any nasty comments, I just told my experence with rudeness and said that I would never do business with this company. The review is listed with my user name (Google user name) as the submitter and no where in my post did I provide my legal name. Once I read the reply to my review and saw my name I contacted the company thu email and asked to them remove my name from the reply and they refuse to do so. Do I have any legal rights if they refuse to remove my name?