We're not married, never will be (because the man is anti-marriage), Fartypants has my surname. We did discuss it quite a lot, so we each understood the other's viewpoint, but it was academic really, because I wasn't prepared to compromise on surname, and ultimately it was my call because I could have registered her alone with any name I liked, and he couldn't.
His view was tradition, mainly. It hadn't occurred to him that in the unlikely event of him having a child it might not have his surname. He'd just assumed it would.
My reasoning was manifold:
In the event of a split DD would stay with me; having different surnames didn't appeal, and nor did one or both of us having the name of someone who wasn't part of our family unit appeal;
I don't like double barrelling (and neither does he), it makes for somewhat cumbersome names;
If he wanted the same name as her he was welcome to change his by deed poll;
Even if we got married I'd keep my own name, so us all having the same name wasn't an option unless he changed his;
There's a school of thought that says a man's name is his own, but a woman's is her father's. Not only do I object to this because it's rooted in the idea of women as chattel, but also his name is his father's just as much as mine is my father's, and his father's a douchecanoe, whereas mine's a decent bloke;
Probably more but I can't remember offhand.
There was compromise though. His surname can be a unisex first name (think 'orrible thick creamy liqueur), so she got that as a middle name. We compiled a shortlist of first names and took it in turns to cross one off, and eventually whittled it down to two. One that I love, that he'd thought of a horrible nickname for and so was dead against, but he hadn't crossed it off during his turn because he knew I loved it. The other, wasn't his first choice but had come from his shortlist not mine. I didn't mind it but wasn't overly enthusiastic about it either. So I crossed my preferred choice off the list.
In short, he picked her first and middle name, I got her surname.