Reading your story, I felt both sad and relieved. I felt sad because you lost your father in 2008, and because you're struggling with certain aspects of your identity right now (the different last names). That can't be easy to handle. =(
But you know what? I feel relieved, because your mother DIDN'T stay with an abusive man, like so many battered women do. I am so glad that you weren't killed as a baby, infant, or child, and that you are here with us today. I am overjoyed to hear that you had a father - and a GOOD one at that. Sure, he may not have been your biological father... but in my mind, it is the man who plays the role of "father" that is TRULY important in our lives. That other man, frankly, was just a sperm donor. He didn't teach you how to tie your shoelaces, or how to multiply 2x6, or why it's important to be honest and true to yourself at all times.
It can be very hard for parents to know when it's "okay" to tell their children the truth. I know that my friend didn't find out she was adopted until she was 18. She always suspected, because her parents were so old (60's and 70's)... but they thought that telling her at a young age would be too overwhelming. They were afraid that she wouldn't understand that it's OKAY to have parents who aren't biologically related to you... that it doesn't make you any less valuable and lovable to those around you. They didn't want her to compare herself to "whole" families, to children who had a "real" mother and father.
It's easy to look back now, and to say "My mother should have told me sooner"... but you also have to try and see it from her point-of-view. Maybe she kept it a secret, because she didn't want your relationship with your father to be damaged. Maybe she kept it a secret, because she didn't want you to go looking for your biological father/family, when there may be some danger in doing so. Maybe she wanted to spare you the emotional harm, and wait until you were an adult before breaking the news.
I don't blame you for feeling the way that you do... but please, don't allow yourself to hold on to these feelings for the rest of your life. The bottom-line is that you had a wonderful father, and that your mother escaped a dangerous situation. Focus on the positives as best you can. Don't become "the-girl-who-never-knew-her-real-father"... be "the-girl-who-lost-a-beloved-father". =)