I didn't change my surname, and in fact, the name I chose (as my first name) was just the feminine form of my old name (Elaine is my middle).
While I didn't have the association of my last name being used as my nickname pre-transition, my new first name is similar enough to my old one that it created that same old-name/old-life association that you have with your last name. First, let me go back to the surname. For me, I never even considered changing it. That's my family, the name I properly belong to, and I felt that changing it would just be lying to myself. That said, I had no reasons that I might want to change it (my family took the transition very well), and after my father past away I was proud to carry on that name. Now, for you, I could see why you would want to change it (the surname). That is a very real association you have there, but remember that everyone will be calling you by your new first name, and the last name won't be used to call you by anymore.
For me, I had originally planned on making Elaine my first name. The name I actually wound up choosing may have seemed obvious (it just adds an 'e' to my old name), but in the past I never really liked the name. As I came closer to transition, it was becoming clear that my family would have an *extremely* tough time calling me Elaine (I have a very close and big family). I started to consider just feminizing my old name, not intending to actually use it, but the more I thought about it, the more I actually liked that name if I was completely subjective (if I didn't think about the association to my old life). Eventually I got to the point that I was able to completely forget about the past associations and look at the name I took as being beautiful, unique, and really truly fitting. On top of it all, I never really felt comfortable choosing a name myself anyway, and there was also the argument that had I been born a girl to begin with, the name my parents would have chosen may very well have been the name I have now, with all the same Latin meaning and all that. Now I love the name, despite its connection to my past. I personally would tend not to recommend changing a surname, but in the end it really does become an issue of personal comfort. Is your last name as it is now something you feel you can ever be comfortable with? For me, it was assurance in my femininity that gave me the confidence to use my new first name with pride, in spite of my birth gender, not because of it.
Also, I should point out that it's probably much more difficult to change your last name without a marraige license or something. The first and middle names are gender-specific and a trans-woman has very good reason to change them, but for the last name you would have to really make the argument that you need a new one and I think the court's main concern would be to make sure your not trying to evade creditors or a loan company etc.
Hope I helped!
EDIT: I just read Lydia's post, and if I were in your situation Lydia I think I would definitely change my surname, too. But if you have any chance of a relationship with your family, than maybe you should keep it? I don't know, I know I'm probably biased because my family has been pretty good.