I'm neither LGBT nor an adoptive parent, but I would say the first and only really important question is whether your child changes his/her name; that is, if she wants to, what the social worker thinks, etc. So I would sort this out with social worker and child first and foremost. (My gut reaction is that the symbolism of changing an adopted child's name is important but shouldn't be done without the child's agreement.)
If the decision is made to change the child's name, then the name you choose should be whatever you and your DH decide--just as it is for all parents. My DH and I have different last names, and 20 years ago (when I was pregnant with #1), we decided to give all our kids DH's last name and my last name as a middle name. (In part because I thought at the time that hyphenated names were unwieldy in our culture and in part because our families were already flummoxed that I hadn't taken DH's last name.) This has worked out fine for us (I've never had any external difficulties or internal angst with having a different last name from the rest of the family), and I have no regrets about making this choice, but if I were making the decision today, I would hyphenate the kids' last name. And if you're looking for advice, that's the advice I'd offer you.
Whatever decision you make about a new last name, you might consider asking your child if he wants to use his current last name as a middle name.
Best wishes to you and your family, OP.
