None of the names are real....
My mother had a birth surname (Smith) and a foster surname (West). She named me after the foster surname (West). Which is weird, because she later reverted to her original birth surname (Smith). I never met the foster family as a child.
My younger siblings had their fathers' surname (Tate).
However, I actually ended up living with my mother's birth mother (she was given up by choice, and later reconciled with BM as an adult). My maternal grandmother had originally been Smith after her first husband, but remarried so was now Lanes.
So, I was the only West. My mother was Smith, my siblings were Tate, my grandparents were Lanes. I felt I didn't fit in anywhere. I changed to Lanes by choice when I was 8.
So, while discussion on what it sexist or not is a relevant convo, I don't agree that "surnames don't matter" and children don't care about having different surnames per se. It certaintly bothered me that my surname didn't match anyone.
That being said, I don't think I'd have felt that way if my mother hadn't returned to Smith for some inexplicable reason. Why name me West just to leave me on my own and abandon the name? Strange behaviour. I think it's nice to share a name with someone. Who it is doesn't really matter, I guess.
I'd quite like to take my DPs name if we marry. I've considered him taking mine but... 1) he's an only child and the name dies with him, whereas my new surname (that I took from grandmother and step-grandfather) is shared by my uncle and cousin's so won't die with me. 2) My new surname is very, very, very common, whereas my DPs isn't. 3) His surname is just "cooler" (compare West to, say Tempest... I'd pick Tempest!)