Little children copy what they hear and please the people they depend on. My guess is that she initially called you by your first name because she heard other people address you that way. For some reason, you didn’t correct her or play with her using lots of phrases like “come to mommy” when you talked to her. Maybe you thought it was cute at first. Maybe you didn’t think it was such a big deal at the time. Or maybe you didn’t understand how other people establish what they are called. Later on, when stepkids entered your life, I’m guessing that they called you by your first name too – which only reinforced that you are called by your name. Whatever the reason, or combination of reasons, your daughter now has 16 years of thinking about you and calling you by your given name instead of by “mom.”
I don’t think she doesn’t love you. I think she’s worried that she loves you too much. Being a teenager, she needs to find some way to declare herself as an individual. She is declaring her independence by pushing at you – hard. One of the ways is by refusing your request. Meanwhile she refers to you as “mom” to others which shows you that she does value the relationship.
You’ve done a great job of parenting her as shown by the fact that she is wonderful in almost every way – except at home. That this is normal doesn’t make it any less painful for us moms when we’re going through it with our teens. Hold on to the fact that she’s so lovely and accomplished. Love her, no matter what but do let her know when she’s crossed the line and been disrespectful. Have faith that the closeness you had is still in there somewhere. It will come back out sometime in her twenties. I wouldn’t be surprised if someday when maybe you’ve given up on it, she starts calling you “Mom.”
I wish you well.