I'm a step child on both sides of the family, my dh is on 1 side.
I just want to say, very cleary, I really disagree w/ the Miss XXX thing. That is the worst thing you could do, in my opinion. That would put a solid wall between you.
What's your dh's issue w/ your first name? If he must have something different, then how about Aunt XXX? That's more of the step-mother's role anyway, adult relative/friend.
If she doesn't already have a room in your home, is there something that can be done about that?
How does she feel about her younger siblings (yours and dh's kids)? Is the relationship close? Blended families can be hard - I hope you can make her feel part of the family, and not a visitor. Does she live close, where more time can be spent together? Even if it's you or dh picking her up from school another day a week, having a snack, doing homework, and taking her home (if mom doesn't want her having dinner out 2x's a week).
there's a divorced family in my dd's class, and the ds lives w/ the mom. When he gets off the school bus at school every morning, his father is there waiting to walk him into school and stay for prayer/pledge (many parents stay for prayer/pledge, so it's a normal thing). I also very often see his dad picking him up from school. His dad is at every single function, parent meeting, open house, (and so is his mom, and they totally don't speak or even look at each other, but they're both there). I'm just wanting to give you ideas, so maybe you'll think of something that could work w/ your family and schedule. I think quantity time is important (just as important as quality time). Sometimes the space between the visits can make a child feel like a 'visitor'.
What about other things that would make her feel like a part of the household? a small allowance, for keeping her room (if she has one) neat. I don't think too many chores is good either though - then the kid has double chores (home and your house). some parents don't tie allowance into individual chores and just give it for being a part of the family, and for just being responsible for oneself (taking your own plate after dinner to the sink, hanging your own coat and putting shoes away, little things like that).
Do you guys make it clear to her that there are 3 children in your household? Her, and your 2 little ones? She might need to actually hear this often. That she's 100% a part of this family. Sometimes we 'assume' other people know things, and they just don't, especially kids.
When you send out christmas cards (or whatever), is her name always on them? Little things like having her sign her own name to a family card might help a little. how about an american girl magazine subscription (or any kid magazine) that gets mailed to your house? so when she comes over, she'll have mail there, at her other house. I'm just trying to think of ways to make her feel your house is her house too. maybe have 'family meetings' once in a while when she's over, just going over stuff like where next summer's vacation will be, where you'll all eat out next month, what you'll plant in the garden in the spring... family stuff that might get decided when she's not there.
hope everything turns out well! it's so great how concerned you are about her and the situation - you're a great stepmom!