Giving baby a unique last name

My husband and I don’t share a last name. I love the idea of giving a child a name that is unique, but also says “we - your parents - chose this together for you”. It’s a way of being both their own, and also a product of our love and consideration.

At the same time, I grew up in a big family, and while I don’t really care about shared last names, I don’t want to assume that a child would or wouldn’t care.

My husband, like me, is keen on either option. We agreed that we would give the child my last name if it’s one of ours since mine is less common than his, and neither of us want to go the hyphen route.

Thoughts? If anyone here has done this I would love to hear your experience in particular!

Edited to add: thank you SO much for everyone that’s weighing in. I really appreciate it and would love to hear more about the details of people’s experiences!