DD has my surname (I'm her father) and I've got mixed feelings about it.
DP didn't know she was pregnant until she went into labour. We'd also only been going out for 11 months at this point. We were also both planning on being childfree, so had never really thought about baby names.
As a result we'd never really thought about names and really struggled to come up with a first name we both liked. We finally found one 13 days after DD was born, and DP said she wanted DD to have my surname because it was traditional.
I didn't argue, I wasn't really feeling connected yet to this baby who'd just appeared (We weren't living together at this point, and I'd missed the birth due to working away and not getting back in time.) Also, the only first name we could agree on really didn't go with DPs surname. It sounded like a superheroes girlfriend ( think Lana Lang, Lois Lane, Pepper Potts type of alliteration)
16 years on, I'm glad that we have the same surname for conveniences sake. Men get treated with suspicion when they're with a small child in a way that women just don't, and having someone ask my daughter her name, and me be able to produce ID with the same surname has been a godsend at times.
(An example, me and DD went to the Harry Potter Studio Tour when she was about 12, needed a hotel room the night before. DP loathes HP so didn't come. Lone man sharing with a young girl in a Travelodge not far from a major airport raised some suspicions, so DD was subtly asked some subtle but probing questions by the receptionist. I doubt sharing a surname was the only factor in the receptionist deciding I wasn't a human trafficker, but it can't have hurt.)
However at the same time, I worry sometimes that DP feels slightly on the outside of the family. DDs personality and interests are similar to mine, and she looks more like me (which admittedly was reassuring when there was suddenly a baby who'd been conceived when we'd only been dating a couple of months). DP hasn't said anything, but I do think that extra signifier of "This child is mine, I made her" would be nice for her.
We should have double barrelled really, but I don't think it even occurred to us in the midst of the other chaos at the time.