one thing to think about is will it be confusing as the kid gets older. i know a few people that HATE that they have hyphenated names. They wish they only has the one name, but the mom kept the maiden name and hypenated the kids names. So you have to think ahead some as well.
More people think I am my stepson's mom because we have the same last name, and because of how we are together. But even as the stepmom, I have NEVER shown anything ANYWHERE. I can get info from the doctor's no problem, take him for shots call the school whatever. Because, if they see you with the child at these places, they will assume you are the mom, and you have a right.
I know my stepson has asked why he is the only one of his mom's kids with a different last name. And my husband made sure that his ex wife DIDN"T change the last name to hers at all. So you could end up with the child questioning their name instead of others questioning you about the name.