I'm surprised this wasn't brought up during your Stage 2 meetings - I know we discussed names extensively. As a same sex couple maybe it's just something that was highlighted pretty early on though -there was always going to be a question about who took whose name, or what we did. As a matter of principle we kept our own singular last names and decided the kids would double barrel ours, and then give them the option to drop one or the other as they wished.
Is there any reason she shouldn't have your last name, beyond any particularly patriarchal assumptions that everyone in the family should go by the male's name? Also, which of his names is he choosing - if it is cultural thing (like in some places in Europe), then surely the tradition is already set? For example I'm sure in some cultures girls are given double barrel surnames from their mother and their father, but then drop their mother's in favour of double barrelling their father's with with their husband's name. The child gets their mother's father's name and their husband's surname. Complicated, but traditional I guess, so there is precedent for which name to take. If it isn't cultural, then you need to think about the choices that are being made - so is it his father's or mother's name your child will be taking? why did you choose that one? What will it say about your relationship with that parent over the other?
I would be very careful about the way other people perceive names as well. Even if it doesn't matter to you, it will matter to other people. I might be the black sheep of my family, and my kids might be the only ones to grow up outside the northern idyll, but I will be damned if I didn't make sure they at least had my family surname so that I could make it exceedingly clear that I considered them my children and my parents grandchildren.
Anyway, how it sounds rolling off the tongue is one thing, but kids can and will change what they are called to suite themselves. I would be more interested in really unpicking the significance of the names that are given, and considering the weight of what you are including or dismissing. Or if you don't ascribe weight to it, know that others might, and there will be questions asked about what you meant as a result of choosing that name.
Anyway our motto was also if in doubt, don't leave it out, so our kids have 5 names. Maybe excessive, but know that your kid won't be the only one!