Actually, I'm not sure I see what the big deal is. I'd accept being called either Alex or Lexi if I was in the same position. Lexi sounds enough like a pet name for your girl to address you with and not with a total feminine conotation. It would be different if your name was John or Jeff but Alex versus Lexi in couple speak is no big deal to me. Would you hesitate to be called darling or honey or dear in public? Now if she called you Judy or Jennifer or Alice that might perhaps be more of a problem. I'd jusr ignore it and get on with your life.
Dawn