how would you feel ... or what should I do ?

I know it's none of my business but ... I just don't know how I feel about the situation. 
My now current BF was once married before me ... and has been separated from his wife for four years. We date and we're happy and everything but what m bothers me most is that his ex wife had his last name srill. Now they have a child together but live in separate houses and he tel me that he doesn't want to be with her & that he wants to be with me... and he shows it everyday. I just don't like that she has his last name still